Of course they will. Even Coinbase and similar sites are already acting essentially as banks (but without the legal guarantees). They keep your private keys for you and provide the paper trail, in exchange for convenience.
When it comes to the financial world, if there is demand for the service somebody will build it (and charge you for it)
What the hell are you talking about? They own your bitcon then. That's a load of rubbish you talking.
I always have this fear of loss, hacks, amnesia ffs. Those worst case scenarios where you have nothing that connects you to your crypto if something happened. In life, if something like amnesia occurred, I would have a paper trail that would say "hey you have a bank account in your name at this bank" or you have an eTrade account with $200,000 in stock in your name". I would have identifications that are within my reach to get. So worst case scenario, even if I lost my memory in some weird accident, protocols would connect me to my money regardless.
So I wonder if there will be a crypto version of these trails. I understand people love the aspect of anonymity with Bitcoin, but it's not like I'm doing anything shady with my money, or don't plan on paying taxes, so I'm more concerned about always having access to money I've stored under any type of circumstance.
You already have access to your Bitcoin at anytime if you in your privatekey. Are you sure you understand how bitcoin works?