Looking back at the history of Vice Presidential picks, at least in modern day politics, it would appear that the VP pick almost always later comes back to bite the President or their party on the rear in the end.
Going all the way back to Reagan, Bush Sr. was arguably the best of the worst because he won one term after Reagan stepped aside. But he only won one term, and then gave us "W" who basically ran the party into the ground and caused voters to go fleeing to Obama. "W" gave us the continuation of the Iraq war and then Afghanistan, and then proceeded to oversee the economy going into the toilet. At the end of his term, everyone hated "W". Now "W" spends all his time convincing the world that voting Republican means you are a Nazi because he hates Trump.
Then came Clinton who picked Al Gore. Al Gore was so horrible, he lost to "W". Nuff said.
And who did "W" pick as a VP? That's right, Dan Quayle, the most disrespected VP in modern day history.
Next on the list is Biden himself. People often joked that the reason Obama picked Biden to prove he could win the Presidency without an actual VP. In fact, Biden had run for President since the 1600's and wound up pretty much dead last every time due to his culmination of gaffs, blatant lies, and plagiarism. Biden was so bad, in fact, Obama refused to endorse him for the Presidency and today is openly favoring he leave office and not run again. The entire DNC is in disarray over him. Unfortunately, Biden is still the same man, only, he can't walk and talk anymore.
So, why is this? I think it has to do with picking someone that is lesser than you are, which is why Biden picked Kamala Harris who is hated worse than Joe according to polls, and is I think the main reason Biden is not inclined to step down. Simply put, you don't want to let that VP pick outshine you in any way cuz it is all about YOU! Problem is, they become the front runner of sorts for the party, a front runner that is going nowhere, or if they do win the Presidency like Bush Sr., it will wind up destroying the party in the end.