Depositors don't stand to benefit from a bank engaging in stupid risky bets with depositor money.
Investors do (on the upside of those bets).
This is why depositors should (and do) have moral priority for their money.
Investors also are able to directly control the degree of stupid risk-taking behaviour taken by the bank, by virtue of their control of the board. Depositors have no such leverage.
If you make depositors (or the public at large) pay for the sins of the bank's management, you get a classic conflict of interest problem. If you make investors pay, it goes a long way towards aligning their interests with keeping the bank running well.
If depositors know that their money is fully covered, you incentivise them to move their money from responsible banks to irresponsible ones. It's easy to imagine a knock-on effect where responsible banks are incentivised to behave less so in order to retain custom, with the whole system becoming more fragile as a result.
Citibank equity holders (one of the the more egregious bailouts from the GFC) 15 years later are still down 90%. So it’s not like in the bad old days of 2008 investors were getting off scot free.