But even if the only option was to use taxpayer money, clearly it would be need to be done. If depositors weren't made whole, this week would've been a disaster with multiple bank runs that could cause a huge systemic issue. Eventually the fallout from such an event would bite the economy and the average taxpayer very badly.
The amount of money required to make depositors in SVB whole is negligible compared to the potential damage not doing so would cause, so it doesn't really matter where that money comes from.