That's a good question. The key is where I wrote that it was a
liquidity crisis.
An analogy: you (hypothetically) keep your money in some 6-month CDs, with about a month's worth of expenses in your savings account in case something unexpected comes up. Then you lose your job and by the end of the month you haven't found a new job. You could liquidate your CDs, but the early-liquidation penalty might mean you still won't have enough to pay your bills. If only you could wait for maturity.
So yes, at mark-to-market firesale prices that means SVB can't pay out in full today to every account holder and so FDIC has to step in. But FDIC (who has a very large balance sheet) also seizes those assets. They give the accounts to another bank. Then FDIC can unwind those seized assets in whatever timely fashion it wants.
There's a second factor: in a secular banking crisis they may pay out only the guarantee (currently $250K; for a while (during the GFC IIRC) it was temporarily $500K. But we are not in a secular banking crisis; not only has the Fed completely restructured bank reserve requirements in response to the GFC but SVB is a single, small bank, not even a regional one, with a run-of-the-mill crisis. This is the kind of failure that you put all the new hires on because they can learn without any up-to-the-minute crisis stress. This is what they learned during onboarding :-). In such a situation it's better to pay out move than the $250K, probably several million, to prevent any "contagion" (since SVB has "Silicon Valley" in its name).
I have no special knowledge of FDIC's internal thinking: they could make them whole now, or make up to $250K whole now and pay out some later, or yes, they could force a few people to take a haircut. Those (small number of) panicing VCs would be better off calling their senators than their portfolio companies.
PS: BTW hypothetical you has more options than those above: you could take out credit card debt, perhaps tap a HELOC you might already have in place, etc. SVB had similar options: they did have a $15B fire sale and got an investment from General Atlantic. It wasn't enough.