Warren may be a relatively left-wing member of a potential Biden cabinet, but I don't personally believe she would "push Biden left" economically. We all know a Biden administration would be stacked full of the same Wall Street execs as Obama's cabinet. The Biden camp have also considered big bankers like Jamie Dimon (JPMorgan, pre-massive heart attack) and Larry Fink (BlackRock) for Treasury. Where's the consistency there?
Warren would just be a token pick to throw to the left, the ideological thrust is in completely the other way. The CFPB certainly ended up being pretty toothless, despite all of her bluster. If I were her, I'd just stay in the Senate.