A lot of my liberal friends are pushing a Clinton-Warren ticket. I ask them what makes them think Warren would have any interest in a VP candidacy when she has said repeatedly that she has no interest in running for the top spot. Then I point out what you just said, and ask them if they believe Warren is stupid enough to think that she would have any influence in a Clinton White House. I doubt she would even be invited to cabinet meetings.
I think Warren might be very amenable to being drafted, but we both know that’s not the same as influencing policy.
Cabinet meetings are pretty rare nowadays. Whatever they want to do, it usually doesn't involve getting 15-25 people with very different portfolios together in one room.
Warren could provide Hillary with a public face for her administration that would be attractive to the Democrat base. Clinton probably wouldn't actually do anything Warren suggested, but Liz might be slow in catching on to how things were.
A lot of politicians are flattered by simply being in the loop. Biden may be the kind of person who treasures and cherishes the few moments when he had any influence over anything at all, and forgets about all the matters that he had no say in. I don't know if Warren would be the same way or not.