It's the right move. If they didn't do it, every regional bank, especially those that primarily deal with businesses (which are likely to have more than $250K in deposits), would be at risk, since the expectation is that your "money is safe in the bank" is what allows the banking system as it is to exist.
None of the other regional banks had the investment risk profile or the depositor distribution (number of individual investors, SMBs, startups) of SVB.
It doesn't matter. The goal is to contain fear, and fear does not act rationally, nor do depositors try to understand all of the intricacies of their bank's risk profile--they'll figure that BoA or WellsFargo will be better because they are "too big to fail".
The fact is that if depositors hadn't run on SVB it also would have been ok.
But in today's economy, any rumor or random event can cause a run on any bank. In fact, there are stories as we speak of the current run on SVB being caused by Peter Thiel and his buddies.
If the banking system is so fragile that it is prone to bank runs on slight rumors, which can be contagious and spread to other banks, what is the solution? To just continue bailing out banks as they fail?
In today's economy, banking -- and by that I mean the basic function of a secure place to put your cash other than having it in dollar bills in a safety deposit box or under a mattress -- may be considered an "essential service", particularly for businesses. The fact is, you cannot operate a business without it. So putting your money somewhere safe (I'm talking cash here, not investments) should be something that is guaranteed. The $250K limit does that for individuals but not for businesses who may need millions in readily-available zero-risk (other than inflation) cash.
This line of thinking leads towards basic banking services being fully guaranteed, and perhaps owned, by the government (like the postal bank in some countries). Banks make money by providing other services on top of that.
Something along the lines of how power utilities work might be a model for the future.