Leveling up seems like a good reason for someone who’s stagnating at a bigger company. My experience is startup people want to recruit their most respected former colleagues, who by virtue of being respected are also getting promoted in place.
Titles obviously don’t transfer back to big companies, we had plenty of ex-cofounders and CTOs hired into the same junior roles as anyone else who could LeetCode.
It depends on the role and company, if you want to get paid 200k per year for the opportunity to do X - then sure. In practice, you may end up doing basic work at a lower quality than a large firm. Such experience doesn't translate the up-leveled title to a more standard position.
And at a large corp you can get laid off just as easily. Any business can toss you out at a moments notice. It's not unique to startups.
At least with a startup you are going into it knowing that you have a higher probability of thing going south financially. With a big company, you might not get any warning at all.