You can't install apps through "normal user" means on the Android phones I've had unless you add an account.

De facto, that means you need an account.

Yes, I know you can try to find copies of your banking apps on apkmirror and sideload, but... no. (Also, wouldn't that mean that you have to manually confirm every single app update, so a 10-minute button pushing session every week?)

Not really. Nintendo eShop and Google Play Service will dark pattern you towards having an account in cases where they don't outright require it like DLC expansions to the "physical" cartridge you "bought".