Is there any service like this for individuals? Specifically, I want to be able to open and close checking accounts at will with different card numbers, with different spending limits. The purpose would be to serve as an envelope system and budgeting tool.
Neobanks sometimes use this notion of a virtual bank account. My understanding is that it's a single FDIC insured account that they subdivide using their own ledger.
For cards, you can use Stripe Treasury or Lithic to issue your own virtual cards and their dev limits are pretty friendly. I think privacy.com does this as a consumer experience really well. Note you said `checking accounts at will with different card numbers`. Depository accounts are a totally different notion and resource than cards.
However should you do this? I can't think of a reason why you'd want to for your own purposes. The reason fintech is so annoying is not because banks/tech players don't want you to have nice things, is that there is a ridiculous amount of regulatory overhead.