There are times when government intervention and bailouts are appropriate, in order to prevent some greater bad for society, or in order to ease the effects of some kind of large-scale economic change.
Bailing out startups is dead last on that list. That is absolutely not something the government should spend tax money on.
Bailing out uninsured accounts in a failed bank may not be, even if they happen to be startups, depending on the form of the bailout. Favorable term government bridge loans against the receivership certificates (perhaps limited to some reasonable expectation of what will eventually be realized on those) would not be unreasonable, and would mitigate the worst short-term impacts.
OTOH, the problem is that for it to work, you’d [EDIT: probably; maybe there is a means to do this under executive authority] need immediate legislative action, involving both the Republican-majority House and the Democratic-majority Senate, and that seems improbable.
Bailing out startups is dead last on that list. That is absolutely not something the government should spend tax money on.