She only gets as much influence as VP as he chooses to give her though. For every Cheney there's a Pence or a Gore (I literally just had to google who Clinton's VP was, because it was so forgettable). You say Biden is disengaged but that doesn't mean his CoS and core team will be, and given that he doesn't agree with Warren on lots of things, it seems wildly unlikely he'd allow her to just take the lead or even have any real say on any of them. Why would he? He can have her on the ticket, pull in some of the progressive vote and still ignore her later.
Re access to power, I'd argue she has much more power as a prominent senator, committee member and senior voice of the progressive movement than she would as VP to a guy she doesn't agree with.