The way the classes are inherently designed in TF2 is that some classes are generally better overall while other classes are better for niche purposes. The classes that are better overall tend to be combat classes capable of winning 1v1's against every class except possibly themselves. Given this, there is some sense in having the generalist classes having a class limit of 2 while all others have a limit of 1, because these classes will be used in general purposes. This also serves to prevent unbeatable last holds with either two heavies or two engies. If valve chooses to go in this direction, the class selection screen should be reorganized into different categories: Combat, Support, Pick, and Defense, where combat includes scout soldier, support includes demo medic, pick (or some better title) includes spy and sniper and defense includes pyro, heavy and engineer. Players would be more accustomed to what these classes would do simply by having the classes be organized in this manner and it would make more sense than the current system.
I think 6v6 currently provides some pretty strong groundwork for a solid system in TF2 and valve should attempt to support it in a manner that makes sense; there is nothing wrong with 6v6 and a lot of players currently unaware to the gameplay and the metagame just need to be primed and prepared for it.