Bloomberg View has an editorial depicting JPMorgan Chase as "a beneficiary of corporate welfare" that receives a government subsidy worth about $14 billion a year. Among Bloomberg's solutions is "Require banks' shareholders to put up enough capital to make bailouts highly unlikely (we advocate 20 percent of assets)."
Another possible approach, not mentioned by Bloomberg, would be to limit the amount of government deposit insurance for an individual institution. There's already a per-depositor limit of $250,000. Adding a per-institution limit of, say, $20 billion might make depositors and shareholders more vigilant about bank capital requirements — a market-based solution rather than a regulator-imposed one.