In fact Cryptocurrency just need to be more accessible and more user-friendly, most people don't have a clue on how banking system work but they are still willing to use it and put their life saving in it, if some entity find the right balance between security and usability, i think this might help but hope that people will educate their self in the future is a bit unrealistic.
You are using too many words to describe a bitcoin bank, which is what most online wallets and exchanges do. Ie, you want to trust a third party with your money, because you cannot trust in yourself well enough to keep it protected.
My answer to this is, are you willing to pay the fee? You should because:
This is a full reserve banking system. Banks "(ab)normally" pay interest to you because, they don't keep your money, and they can go bankrupt, because of the scam known as fractional reserve banking, which is how modern banks operate.
If you have used debit/credit cards or any type of pre-paid card you put money into it and then later spend by swapping to machines, you already understand the gist of the matter. The difference here is that crypto is far more secure and impossible to fake, as sometimes happens to these naive digital payment systems (ie. for metro/trains/bus etc).
Perhaps for some people some form of hardware wallet would be the easiest to use, only for small amounts of course. A smartphone could accomplish the same function of course, but for some people some sort of "card like" device (with eink screen, reader, etc) would do.
But this is not even the coin's realm, its the people doing the wallets, both software and hardware. The coin itself is good. Already bitcoin is on the brink to be easily used for quick small transaction, via LN, but this LN needs to be implemented in a way that is super simple to use, and that lies in the hands of wallet developers. You can't expect a common user to be running a bitcoin and lighthing node in their smartphone, even if some have already done just that, bandwidth use is prohibitive. That's why light wallets like Electrum have their place for daily mundane purchases at the shop etc.