The government wants it to not be a possibility. Bank accounts are meant to look safe.
If government didn’t make it clear they were stepping in here, what do you think would have happened first thing Monday morning? Every small/medium business would have seen the writing on the wall and moved their funds out of small/medium banks and into the handful of “too big to fail” megabanks. Stepping in and making up the cost prevents contagion.
The 250k limit is somewhat of a red herring. If every depositor split their funds up to stay under the 250k limit, it doesn’t actually change the overall risk profile for the FDIC.