Is there a problem with “problems”?

To answer your question, finding the problem is the first step for any entrepreneur.  That's why customer discovery and product market fit are so important.  Learn how people operate, identify their problems and develop a solution that a) people will use and hopefully love, b) can be defended and c) can be monetized.  If you can do those 3 things, then you have the basis for a successful company.  Miss any of them, then success may possible but is much harder.  

No, it's not necessary to start building a startup from a problem.

There are two types of problems:

Do something you think people will use (and pay for, or otherwise do something revenue generating with), and then verify that they use it. That's more the essence of product market fit.

People generally know what problems they have, but if they don't know a solution is possible, they may consider it impossible and not ask for it and talk about the problem. In that sense, visionaries have a role of imagining solutions to products that customers are not currently thinking about. However, even though the public may not realize the problem gets, there really needs to be a problem there or there will never be a market, and the visionary had better figure out what problem they are solving, the number of people who will acknowledge the problem once they see it and be willing to pay for a solution, or they risk sinking a lot of money into a business that won't return a profit. For creative people it is very easy to imagine things not currently in existence. But sometimes the reason they aren't in existence is not because no one has imagined such a thing, but because even once you make such a thing no one cares! This is the most common outcome for start-up "ideas". And it is expensive to create a company only to find that out, when you can run a few simple "marketing experiments" and find out. For example, let me imagine something that doesn't exist today. Once upon a time, most every car had a gas tank. In a pinch, if a car was stopped beside the road out of gas, you could run a syphon hose from one tank to the other, and get enough gas in the tank of the disabled vehicle for it to reach the next service station. Now there are all electric cars brands like Tesla, that don't have gas tanks. They can't refuel cars that are out of gas. As a visionary, I imagine placing a gas tank in Teslas, because it would allow Teslas to do something they can't do today, but which most other cars can do. Is it a good idea? If you ask Tesla owners "if I put a gas tank in your trunk, for free, enabling you to refill out of gas vehicles, would that make your Tesla more desirable for you?" I predict most Tesla owner will say no, and that even for free it will be hard to find owners who would volunteer for the free conversion. Let's say I come to you with my proposal to build a company that makes and installs these gas tanks. How much should you invest in verifying Tesla owners will really buy my gas tanks before totally committing to funding my business. Contrast this with a very real (unidentified) problem that my co-inventors and I recognized and which led to a completely new class of products, not previously asked for by customers. But because customers responded enthusiastically when they experienced the solution the company was venture funded. It was early 1998. The first commercial web browser was about 3 years old. Homes and offices did not have broadband. The fastest dial-up modems were 56K. It was before the rise of the Dot.Com companies, there were no web videos and even most web pages had only limited images. There was an existing need, and existing solutions: Marketing Managers wanted to demonstrate and promote their new products. They had several ways to do so. Some traveled to 25 different cities each year, rented ballrooms in hotels for up to 100 prospects or sales people, and presented in city after city. The cost of travel, hotel rooms, etc. was high. Sending printed brochures was cheaper but less effective. Telesales was also cheap but not very effective, especially when people wanted to visualize something -- like how a software product's GUI worked. Video required expensive cameras and lighting, and trained camera people, usually had to be in a studio and then was distributed over broadcast TV (infomercials) or through expensive business centers. Into that world, my co-inventors and I introduced web conferencing. No one was asking for it. But as soon as they experienced it, they saw that it was a convenient, time-saving and expense saving alternative to business travel for marketing. It was a new not well understood solution to an existing well understood marketing problem. Because people werent already familiar with it, the service was hard to sell at first, because no one was searching for "web conferencing", in fact, no one knew what those words meant. So you had to find people willing to have an extended conversation to help them understand. But even that didnt help because really it was an experientially different solution, and you had to experience it to know what it is (now of course it is commonplace). Luckily, it was very easy to give a free demonstration to prospective buyers, and it didn't take a lot of explanation for people to understand "what problem it solved". They instantly got that the things they hated about business travel (inconvenience, wasted time, expense) could be eliminated, and instead they could "present" their products from their home at any time, even in their comfortable pajamas. Participants immediately knew what it was good for, and they could rapidly compare the cost and convenience against continued business travel. It didn't sell itself (no product ever does), but trial users did sell themselves. It was understanding that lots of people had this problem, considered it severe, and readily paid for an alternative solution which made VCs think it was worth investing in. The "idea" of web conferencing wasn't interesting to VCs. The "traction" we were able to generate with early users was what interested them. This is why you should start by showing there is a market, with a well defined need, and proof that when offered your alternative solution, people enthusiastically embrace it. Not because it is a good idea, but because they love the new experience more than the old one.

The missing thing in calling it a problem is the fact that you can sometimes enable them to do something which they didn't even know they needed yet.

I see points against thinking of all opportunities as "problems", but looking at it from the visionary / inventor / engineering point of view, every improvement can answer some form of "problem".  Some are apparent to potential customers, many are not directly or at all.  Sometimes, a potential solution makes something more efficient or causes something to be better.  That gap between status quo and a possible future is a problem to solve.  While you can be precise about the difference, I'd only do that when the clarification matters; otherwise, I'd lump all opportunities under "problems to solve".

However, I have sometimes talked to people who think the only valid target is something that potential customers explicitly know they want.  That's a very small, although sometimes significant part of the possible solution space.  Even if people experience pain, their limited awareness of what is possible prevents them from considering it potentially solvable.

My understanding: Focusing on near term problems generally produces small scope vertical "solutions" that are not really integrated with the greater environment. Integration is very challenging. That’s why the eBay market is not really connected with the Amazon market, creating other problems like fragmented reputation, duplicated conflict resolution, etc. I like to think that greater integration engenders a denser and more patterned structure of connections, which engenders more emergent behavior and products.

Couldn't have put it better Scott "You are correct in that most people may not be aware of the "problem" or at least they can't verbalize the solution that they need. That's because they create work-arounds to deal with the problems and these work-arounds often become so ingrained that people no longer recognize the pain. But that's the entrepreneur's job - observe the customer, identify the pain points, develop a potential solution and then create an MVP to test with consumers to see if your proposed solution actually meets their needs and solves their problems."

Importantly, solving a known problem and addressing something people don't know they need yet have two very different dynamics in terms of marketing, channels, competitive landscape, and even market analysis. I suspect that existing problems get funding more often due to the greater number of known variables and the ability for the funder to potentially relate to the solution. The other sort, when they succeed, are the ones that "come from nowhere", like Airbnb. They came from nowhere because no one believed their model actually made sense before they went out and proved that there was indeed demand for their service.