Gosh, it was sooooo big of her to offer.
Joe has a tough assignment: pick a running mate who will excite the extreme left wing of the Dem Party (i.e., most of it) without terrifying whatever passes for moderates and independents. But because of his patent mental decline, Biden must pick someone that all those voters can imagine becoming President the hour after the inauguration, and who can reliably deliver some critical electoral votes. Warren? Harris? Stacy Abrams? Moochelle? Jarrett would be more credible since she has experience pulling Obama’s strings.
It won't be Jarrett for that very reason. Jill does the string pulling around the Biden house.
And along that line, I don't think Jill or Biden's handlers will let him pick any woman that will threaten him, over-shadow him, or try to overthrow him (and that would rule Abrams out. She's threatens everyone and everything. She's a beast.).