What would that accomplish? At least in terms of electing a 3rd party president, that is? Without a single representative in Congress or the Senate, how would they get their legislative agenda passed? Electing a 3rd party as president, would result in a lame duck administration. Whoever actually controlled Congress would simply ignore the wishes of the president, and enact their own legislation...and the president would have no power to do anything but veto all of it. Literally nothing would get done for the next 4 years. How does that prove to the public that 3rd parties are even effective? If anything, it would prove the opposite.

If a 3rd party wants to even have a chance, they need to fill more seats starting at the bottom, and work their way up to the highest office...not start at the top, and work their way down.

This isn't even a matter of principle, either. Without 3rd party support at the state level, there's no guarantee that they'll be given fair treatment in local elections. All the shenanigans that the two main parties get up to, to keep 3rd party candidates out of the race, are because those elections are controlled by the two main parties at the State level. Until there are more 3rd party representatives in State legislatures, they will always be locked out of certain races.