I understand your idea with your first paragraph, but it also ties Harris down to the White House instead of freeing her to campaign, and get her own name out there. If there are any events beyond her control, while she’s President, she would also be on the hook for those.
Biden’s actually pretty good and he is, or at least his staff is, getting a lot of positive things done, as long as he’s off camera. That’s been true throughout his career.