I think that is a fair point. There have been many good Doctors and many of the polls of popularity do have recency bias in them. Although I think it is hard to argue that usually it was 10 and 4 in some order after the modern series got going.
I think for me it is not that there cannot be good Doctors because there no doubt can be. I am sure some great ones are out there. The writing has to improve and the show runner has to worry more about quality of the product or it is putting lipstick on a pig.
I also think in some ways the show has suffered a big since 10 and 11 because Tennant and Smith were both really good at quriky, high energy but can change emotional states on a dime. So you bought the child like innocents and sudden shift into angry old demi-god situation. Eccelsten was good at this too, but it was more pronounced later.
I feel a new Doctor would almost be better served to find their own voice and not try to mimic a popular Doctor. I though Capaldi was not as good at that and Jodi Witticker is really just playing a poor reflection of 10 and 11.
They should have broken the mold on the new Dr, and gone either for a minority Male, or else a teenager Dr!