You're correct, in that it was not immediately clear whether SVB warranted the systemic risk declaration. However, it should appear clear that fear is very contagious and it has never been easier to move tens of billions of dollars of deposits with just a few button clicks. This poses a sincere risk to banks not already declared Systematically Important Banks (SIBS). The Treasury and Federal Reserve correctly intuit that it would cost far more to the real economy, and to tax payers to cover the cost of SIBs then it would be to signal that uninsured depositors will be made whole.

Your claim that "those who believed in the honesty of the system got burned again", is not entirely true. Equity and debt holders have been completely wiped out. Compared to the Trouble Asset Relief Program (TARP), in 2008, this barely constitutes a bailout. Furthermore, if the Frank-Dodd stress test requirements for banks with greater than $50 billion had not been relaxed in 2018 to $250 billion, then SVB and Signature bank would have been seized and sold off well before there was this bank run. It is clear that even smaller regional banks need to face the same rigorous stress tests that SIBs face.