The reason it doesn't exist is business model, not regulatory. (In fact the only reason that API or other conveniences such as PSD2 in the UK would exist is regulatory.)
As the SVB episode has most recently demonstrated, in fractional reserve banking, an individual with a deposit account is not a customer of that bank. They are a creditor. More importantly, as with users of free services, they are the raw materials from which banks create the actual products- loans- for their actual customers- businesses- usually- to whom they lend.
Consumer banking, ironically, is not a business any bank actually wants to be in. It is a loss leader, complicated, and inconvenient.
Individual level API access to deposit money is on no bank's top 100 (or 1000, or 10000) to do list.
