@snood,
I share your disgust at the prevalence of this sort of thinking. After all, should his age become an actual liability in the performance of his job, we have an elected vice-president and the 25th Amendment if needed.
The list of effective and potentially effective candidates for political office who've been jettisoned by their party or rejected by the electorate is, as you know, long. So given this tendency of parties and voters to support or reject office seekers for superficial reasons it's understandable that people who voted for him and even people who are happily surprised by Biden's successes might still feel tentative about his running for a second term.
Hillary Clinton is a smart woman and was an effective senator; she could have held on to that seat through several election cycles. But something happened when she became a presidential candidate. Suddenly, her being smart and effective was overshadowed by twenty years worth of political baggage (more accurately "garbage") that had been carefully packed away by GOP operatives for just this sort of occasion. And even though I voted for her, I had this nagging vision of her prospective presidency being a four year long Benghazi hearing.
Opinion polls show a slight increase in Biden's popularity but nowhere near a level commensurate with his accomplishments. It's frustrating to look at the level of job creation, for instance, much of it directly tied to his policies, and the see the Republicans denouncing Biden for being a "socialist". It will be interesting to see if he'll try to stand above the fray or whether he'll choose to engage forcefully with his opposition. If he chooses the latter, but comes off as old and awkward, I expect he'll have a hard time with the right-wing echo chamber, late night comics, and possibly younger voters. It saddens me as well, snood, but that seems to be the political world we inhabit.