Pim notes Mal Waldron, and Ethan Iverson (formerly) of The Bad Plus has described the considerable influence that Waldron had on his development. But Iverson has also pointed to bop pianist like Bud Powell and Barry Harris as influences.
I think the three pianist named in the original post are very different. Not sure that's there's going to be a singular common root, aside from the broad spectrum of history, with each of them mixing their own cocktails from it.
... Eclecticism rules the day, then and now.