I can't imagine Larry Blyden on Family Feud, unless it was modified to suit his talents. I don't believe Larry Blyden ever hosted a show that just had civilians, so maybe Feud would've somehow incorporated celebs? (Maybe not necessarily Celebrity Feud, but a celeb playing with family members.) Also, as charming of a guy as Larry was on camera, I've never seen him act quick witted, and I can't imagine how he'd handle all the dumb answers family members might give.
I wonder if Richard would've been willing to share the spotlight with a female host. Perhaps if it was his girlfriend at the time, Jody Donovan. However, I can see Richard hosting The Better Sex. I can't see him hosting Make Me Laugh. He'd be more at home as a panelist instead of the host. I don't think he'd like 3 comics that try to be funnier than him. Bobby Van was a great straight man, and that's really what Make Me Laugh needed.
Beat the Clock... well, again, if the show was tailored for his talents, Richard probably would've done well with that show.
Richard Dawson and Gene on MG/HS? No, it would never work. Hollywood Squares worked best with a straightman hosting. Richard Dawson is DEFINITELY not a straightman. Would Richard have been on the panel if he hadn't had success on Feud... maybe.
Who knows WHY Jon Bauman got the nod to host HS. I think when Peter said he did an all right job in his book, he was being kind. I can sort of see the logic of why John Davidson was chosen to host HS. I think in the beginning, John had reasonable control over the celebs, and he certainly kept the game moving at a smoother pace than Jon Bauman did. John was a semi-regular on the original HS, so it made sense to hire someone that was familiar with the original show. John Davidson was also a very good HS panelist, and one of the show's best bluffers.
I think in the show's third season, John let Jm. J, Shadoe, and Joan overpower the show, and it got stale.