The problem I see with your suggestion is: How do you know or control that the employee didn't download the company's files to their computers and stored them on a USB pen drive? Which means, if they left, they kept that info. Regardless if you have it in the cloud or not.
It's true, that the employee can also do the previous with a company own equipment, but at least, the company will be legally more protected than if the employee used their own computer. Unless you do Lorne's suggestion.
From an startup point of view, having employees use their own equipment is a huge money saver, I'm guilty as charged. But that benefit, obviously comes with some important risks.