By far the most important thing about the VP pick is his/her ability to help get the ticket to 270 EV.
Any other consideration is a distant second in importance. The President can shape his circle of advisors, cabinet heads, etc any way he wants once elected. But he has to get elected.
Adding to the ticket’s chances at 270 EV requires that the VP nominee have significant key state, regional, or key voting block appeal. And oh yeah, he/she has to be a credible back up POTUS.
Key state appeal is hard to game but it could be vital.
JFK running with LBJ to secure TX
And hypotheticals:
If Al Gore ran with a popular Florida democrat in 2000 he would have won.
Ditto for Kerry and a popular Ohio democrat in 2004.
OTOH Mitt Romney would have needed about three such VP nominees in 2012.