Brian Beutler at the New Republic makes the case for Warren as Clinton's most "rational" choice for VP.
What Warren lacks relative to Kaine in executive experience she makes up for with a clear, consistent, and progressive ideology. President Kaine would likely be a fine president, perhaps a great one, but his slate is much blanker than Warren’s. Democrats at the elite and grassroots level know what Warren’s substantive goals are, and have responded to them enthusiastically.
Moreover, Warren really rattles Trump. And her progressive ideology should help snag Sanders' voters.