Wide breadth of skills? If you’re hired as a code monkey you’re going to monkey code. Nobody ever asked me what I thought about the latest business partnership or synergy strategy. Just code.
Career progression? Another nope. With only a few people in the company, you can’t go up and you can’t build a team under you. Who are you going to manage? There’s nobody under you! My startup coworkers used to jokingly give each other fake “Senior Director” titles which were meaningless of course because there were two managers in the whole company, one was the CEO. Even if you did somehow get a fancy title or a team under you, and got bought by a big company, you’re back to “3rd engineer from the left” in their hierarchy.
Hard problems? I don’t know, not in my experience. Just problems unappealing to the bigger players.
And for all that you risk the company not being able to make payroll or canceling your benefits. Sorry, I can say definitively that working at small companies probably set my career back 10 years.
EDIT: I suppose it’s highly dependent on the company.