Nicholas Beaudrot follows up on this by saying that we should triple the size of the House of Representatives. Jonathan Bernstein has some interesting critiques of Beaudrot's plan (here, here, here, and here), although he does claim that it would increase the percentage of women in the House. I'm not sure why that would be the result of shrinking districts -- it's not like our state legislatures are teeming with women.
One thing that would likely happen with a mega-House is that the tools that legislatures use to organize an unruly chamber -- notably parties, committee chairs, and the speaker -- would become stronger. I don't know that that's necessarily bad or good. I suppose the main advantage of the reform would be to improve representation. Members would have smaller, less diverse districts, and they could conceivably meet a high percentage of their voters. That's not nothing. But would it be worth the size of the reform? (Think of all the work that would have to be done to the chamber itself. Plus, if we still paid members at their current rate, we're talking about an increase of over $160 million in member salaries alone, not to mention staff.)
Oh, and nothing personal against Joe Biden, but we really don't need a vice presidency.