Where else would you keep track of your money? MOST currency is digital these days, and somebody has to be the keeper of the records.
Your employer doesn't hand you a bunch of cash on payday - they either give you a paper check, which is simply a theoretical representation of cash, or they make a direct deposit into your bank account, which is another representation of cash.
In the days before computers, your "money" in the bank was just a ledger entry that some underpaid, overworked clerk would notate whenever a transaction occurred. How's that any different in practice from what you're talking about? When you bought your car from Ford, did you haul cash to the dealership, or did you sign a piece of paper that simply transferred electrons from a lender's account to Ford's?
There has to be a trusted third party who keeps track of who owns what, and nowadays it's largely digital. If you want to make a large withdrawal in cash, you generally have to notify your bank in advance so they can arrange to have it on hand when you come in for it - rarely would any bank branch keep enough on hand to satisfy more than what it estimates is the average daily requirement to fulfill withdrawals.
Interestingly, my local branch of Wells Fargo actually RAN OUT OF CASH at one point yesterday because so many people were showing up to withdraw their stimulus deposits, so there was a brief period when they couldn't honor further cash requests until more money was delivered by armored car.
Since banks loan out your deposited money, none of them would EVER be able to meet demand if everyone were to show up and demand withdrawal of their funds in cash. The point is, it's all theoretical and digital now.
To your point about "hauling it around on an SSD", what do you think most people who hold cryptocurrency do? There's no "bank" per se, and no asset backing it of any kind. If you lose your digital wallet with cryptocurrency, your money's GONE. Witness the list of incidents on the web where people have trashed their hard drives or lost their computers and as a result lost their crypto holdings. It makes sense, then, that you'd use some form of "cyberbank" to hold on to it for you so as to make sure that doesn't happen, right?