I’m surprised they didn’t make more of a big deal of River using up her regenerations on him, since as far as we know she’d only regenerated three times there’s 9 more incarnations there! Frankly however much I loved the show, I doubt it can really go beyond 20+ Doctors.
Well, there's another interesting question! Even if regeneration isn't capped, realistically, how many Doctors will there be? Undoubtedly, the show will be cancelled at some point.
The original series had 26 seasons. The newer ST franchise ran various incarnations for 18 years. Somewhere around there seems to be the maximum length a franchise/series can go. If you split the difference and figure that the new series of Who will go 22 years, that means we'd have 15 more years from now.
If you figure an average of 4 years per actor, you've got 3 more Doctors, for a total of 14. If one of the actors remains for several years longer than average, the series could end naturally with 13 Doctors.
Highly speculative, but agree that it would be nearly impossible to get to 20! Of course, the series could stop and then be restarted. That's been known to happen!