The depositors will be paid back by their own money. The money hasn’t disappeared anywhere. It still exists, and the bank will still make a profit as the MBSes it paid into will continue returning money to the bank. It will simply make a profit that’s less than what it could have made with the same shareholder equity with way less risk in other investments. Which is why shareholders got wiped out.

This was a classic bank run. A combination of the concentration of depositors from a single industry, massive swings in the monetary flow of that industry, poor investment decision making, and having regulations loosened on it meant that SVB saw far too many short term depositors call for their money and had too much of that money tied up in long term investments.

The government has the liquidity and the reputation that is needed to prevent this from becoming a problem.

The cost that is being borne by the taxpayers is the cost of people depositing money in smaller industry focused banks, which have greater risk, and lower efficiency. If you really wanted to eliminate the cost, the solution would be to have everyone deposit their money in a handful of Too big to fail banks, which would almost certainly be cheaper and more efficient, but is also a bad economic system because of the political power those entities gain.