Is it illegal for banks to provide private customers personal API access?
Under the "open banking" scheme, not even massive companies can get API access to their own accounts. It only requires banks to give service providers access that allows their customers to essentially OAuth login into those services with their bank accounts. There is no "I just want my own account" API, only the general one.
And becoming a licensed provider is insanely hard because it's assumed you'll be actively managing millions of euros for tens of thousands of customers, when in reality, all you want is read-only access to one or a few affiliated accounts.