Biden's following public statement, made years ago when his mental faculties were unaffected by signs/symptoms of dementia, revealed his racist attitudes. His words mean more than anything to get inside his head (even now, when he's referred to his sister on stage as his wife, not remembering the name of a senator he's known for decades and greeted her as "senator"...she laughing politely when Biden added "You think I'm kidding but I'm not" (acknowledging he had in fact forgot her name), forgetting the name of the Pentagon ("that institution"), etc...but this quote was actually shocking and it stuck with me and millions more- “I mean, you got the first mainstream African-American who is articulate and bright and clean and a nice-looking guy.” Had I been Obama, I would have scrapped Biden as VP immediately, regardless of appearances...but that's just me. How Biden even obtained part of the black vote is absolutely no comprendo.
And yet Obama twice sailed to victory with Biden as VP, and Biden enjoys approval ratings over 50%, a feat never achieved by Trump and only achieved by Bush right after terrorists attacked us. So maybe there are some fatal flaws in your theories.
You are right to imply that Obama obviously determined that Biden would help him win and by that he helped pull in left and right moderates. It's been said, by more than one source, that Biden's senatorial voting record often resembled a slight of right during the 90's...pretty much what's been said about Clinton during that same time. Biden voted to remove the needed safety net for investors by backing a bill that supported that mega-banks were too big to fail. Horrible bill for so many reasons.
So yes, Obama kept Biden on for a second run and won again. I voted for Obama the first time, not the second for the record. Biden was not a factor in my consideration either time, as Obama had the longevity odds to survive much longer than his VP choice.
I question the validity of Biden's "50% approval" rating. Was this poll cross-sectional as in not just conducted within one state or an even smaller area? Were the numbers polled large enough (like more than 10,000) and were they from various sectors not just one? How were the questions worded and how many possible answers per question? That matters as much as all other factors if not more, as all polls are bogus when the questions/possible limited answers skew the validity all of the way down into the trash bin.
Look at the following differences, but relatively the same question: "Do you think Biden is doing a good job? versus, "Do you think Biden is doing a good job, considering what he's up against?" The first question is more straight forward but would still need a sufficient number of possible answers to attempt valid results. The second question strongly suggests that "bad things" are just happening that are outside of Biden's control, and would significantly change the answers in a more "positive" way most likely.
How many answers were possible to all questions? When given a multiple choice format, pollsters know how to wind up with a more positive result by wording the questions, selecting the answers they want to bolster or minimize a certain result.
I'm still awaiting the various pollster orgs to come out and formally apologize to Hillary and her fans for declaring her to be the absolute, without any question, winner prior to the 2016 election! lol