...and thus picking Rubio may have been useless..
A state-elected official will have more appeal than somebody who was elected and represents only 1/8 of their state. There is a reason Congressmen are rarely picked. They do not bring any real bumps to the ticket in the home-state and should only be picked to beef up some quality that the candidate lacks (see GWB picking Cheney).
Another is that Congressional Representatives have never won statewide elections, except in at-large states that are almost never microcosms of America. For much the same reason, big-city mayors are almost never selected for VPs even if they have administrative experience. If they don't know how to run a statewide race for Governor or the US Senate, then they don't know how to run for President.
Selling people on political change is rare in the House... but in the Senate or in State Houses, politicians can hone that skill to maximal sharpness.