That first question is great one. If Bob had retired a decade sooner, I don't know if the show would have had the success it does now, but I think it still would've been on the air today. Probably after a number of hosting changes (to go along with staffers, the cast, and front office), they probably would've settled with the right person. Took some time for Fremantle to get it right with Steve Harvey. IMO, TPTB were fortunate with Drew. I'm not going to say lucky because, while I probably wouldn't have bet him to be Barker's successor before someone like Marc Summers, Todd Newton, or even Rod (well before he left us), having seen Carey's stuff for a long time before he became host, I knew they'd be alright. Save for the lack of optimism having to follow a legend who'd been there the past 35 consecutive seasons.
To answer your second question, that's a little tough. Twitter and Facebook did exist while Barker was still the host, but social media wasn't a big deal until after he left. It would be rather difficult to see him continue had this continued in 2020 at his age, but I don't know if anything would've happened on his end if the accusations happened in today's climate.
IMO, I really don't know. As mentioned, people have been given second chances for doing worse things. The fact is, there are consequences for people that do questionable things. For me, I see Bob Barker as a great emcee, someone I respect and grew up watching. Similar to every other person on television, what happens in their personal life is none of my business.
It sucks that the negativity toward Bob is there. It is what it is. Can't say it's good, and I feel bad for those that may have been victims or were offended. I agree that it isn't cancelling out his body of work. What I saw for decades was a host that took something huge and made it his own, this after several years of success in non-price stuff