I'm going to agree with Balik and Richards. IMO Richards was the best of the bunch.
You mention Trebek talking about Betty White. I'm sure that was in jest.
But during an interview, he said three names that he felt would be good replacements for him:
CNN’s Laura Coates, LA Kings announcer Alex Faust and TCM’s Ben Mankiewicz. In that interview, he wasn't being funny.
I said the same thing earlier in this thread. I would of liked to seen Jeopardy give these three a week (or two) as guest host.
Perhaps the host of the show for 37 years seen something in these three that would of made them a better fit than the guest hosts we have seen so far.