The comparison between Carter and Kelvin/Tait seems inaccurate. Tait and Kelvin had an incorrect hypothesis but both did a lot of good work. Carter has a hypothesis which has been discounted for a long time and nothing else. Moreover, when Tait was doing his work, the hypothesis seemed plausible given what was known at the time. It took years to understand atoms enough to know that their hypothesis didn't work. The situation is not similar to Carter's.
Freeman Dyson writes in the New York Review of Books about people who took up the crackpot offer. Not just complete cranks, but eminent scientists such as Eddington who got into crankery in their later years.
New thing I learnt: Dyson was not only a good friend of Immanuel Velikovsky, but considers him a greatly underappreciated poet.