I'd like to offer a different perspective. Some people don't care about titles, but many other do and want to manage perception. On their LinkedIn profiles, I've seen people list "Head of [X]" pretty liberally after their formal titles, (in some cases even if they also happen to be "Tail of [X]") as a way to juice up their position.
If you're a founder/exec at an early stage startup, attracting talent is a (arguable "the") key activity that will consume much of your efforts. If an engineer gets value from saying they are part of the "Founding Team", and it doesn't cost you anything, then that seems to me like a win-win. Occasionally at larger companies people will say they were part of the founding team that worked on a given product. That seems OK to me, no harm done. Maybe if you're employee #200 it's disingenuous, but not enough to crack down.
The role of startup founder is somewhat more narrowly defined. To me, a founder would be anyone who is willing to forego all/a significant portion of their cash compensation in exchange for a good chunk of equity in the company, and is expected to play an important role in the ongoing success of the company. Even if they weren't there on day 1, eg if you hire a key member of the exec team post-launch or after a seed round, and they want to call themselves a founder because they see value in the label, why not let them have it? The ultimate truth will be in the cap table.
One last comment: often you see another kind of title inflation, such as founders who adopt grandiose sounding titles, only to have to take a step down (or be pushed out) when the company grows and needs more experienced people (eg don't call yourself CFO if all you're doing is maintaining the Quickbooks Online account). I'd recommend that, once the required officer roles (eg President) are allocated, often to the same person, everyone else should adopt a reasonable/defensible title that you can grow with over time.
Hope this helps, but feel free to disagree.