Well, there is legislation before Committee to mandate open APIs that any accredited institution can use. As a consumer you will not be eligible, but you will be allowed to pay some third-party to pull your data from your bank and save it in their database, after which maybe they might allow you to download it in their proprietary format should they choose.

Me, I use plain-text accounting (hledger) that automatically imports the CSVs from my bank and categorizes transactions automatically, and I wrote some quick scripts using Python to import the PDFs from my brokerages and paystubs. It's not automated pulls but I only have a handful of accounts so it's really not a pain to manually pull statements once a month and run the import scripts. It takes me longer to reconcile everything to the penny then it does to do the imports, and it's a whale of a lot faster than manually entering through GNUCash. Plus, it's plain text so all you need is vim, git, and the command line.