The stuff you describe pretty much sounds like a bank. Instead of a regulated FDIC backed institution you want to store your money at some wallet service which may or may not get hacked in which case you lose your money.
It's very different from a bank, primarily because consumers/payers don't deposit anything, they keep their bitcoins on their device.
Only merchants, who want to receive extremely cheap Bitcoin payments -- the fees are set by the market, but a thousandth of a cent is completely reasonable -- can choose to trust one or more issuers. They may redeem/"cash in" the payments they've received at any time; the more often they do this the less the risk but the higher the fees, but they choose their own risk profile. And if the worst comes to the worst, merchants lose a week/month of income (if they choose to redeem every week/month), the issuers dies, and the merchants will probably survive (assuming the lost income is not fatal to their business). So the bad issuers are flushed very quickly, and merchants can adjust their risk/fee ratio as they desire.
> But if you don't trust yourself to keep your bitcoins safe, you're free to deposit them with someone you trust.
^ This is you, saying that people would deposit things if they fall into the same category of "most people" that don't consider the idea of trying their damndest to just be extremely careful with their cash (which, once stolen, is simply gone, and which can even be misplaced) to be a sane choice in comparison to using... a bank.
Only merchants, who want to receive extremely cheap Bitcoin payments -- the fees are set by the market, but a thousandth of a cent is completely reasonable -- can choose to trust one or more issuers. They may redeem/"cash in" the payments they've received at any time; the more often they do this the less the risk but the higher the fees, but they choose their own risk profile. And if the worst comes to the worst, merchants lose a week/month of income (if they choose to redeem every week/month), the issuers dies, and the merchants will probably survive (assuming the lost income is not fatal to their business). So the bad issuers are flushed very quickly, and merchants can adjust their risk/fee ratio as they desire.