I could be a cog in a giant corporate machine, or I can have a measurable impact where I work.
I can stay in my lane and do my specific job tasks, or I can run around putting out fires and helping wherever help is needed.
I mindlessly build the specific design product handed me, or I can guide my own work in accordance to the needs of our customers and the business.
I can follow policy and fill out forms when making any decision, or I can just do what's right because who has time to write policies and look over approval forms?
tbf, tech is relatively good at a lot of these. As I understand it, Facebook gives a fair bit of latitude to engineers, and Google used to be famous for their 20% time. But the longer a company exists, and the bigger it gets, the more bureaucracy and controlling it'll get. Every big disaster means a new policy on how to prevent future disasters.
I think pg wrote an essay stating that the most valuable skill in an early startup employee is "helpfulness" (maybe not though -- cursory search didn't find it). You do what needs to be done.
This is roughly your "wear many hats" point, but more than just different technologies, and not just being new. If you just want to have a well-defined, steady, sane-every-day job, a startup is terrible. If you every want to say "that's my job", a start-up is terrible. If you're the sort of person people will come to for help with whatever comes up (and enjoy being that), start-ups can be great.