I was also with a provider that didn’t offer API access for the longest time. When they then increased prices, I switched, now paying a third of their asking price per year at a very good provider.
I guess migrating is difficult if the provider doesn’t offer a mechanism to either dump the DNS to a file or perform a zone transfer (the later being part of the standard).
Can only recommend INWX for domains, though my personal requirements aren’t the highest.
Lack of training data