Although I don't play competitively, I understand that the engineer and pyro are not used, the spy and sniper are rarely used, and the heavy is less used. There are several factors why this would be so: small team sizes, 5 CP maps, high level of coordination, and superior playing skill (especially DM skills).
The engineer is the first casualty. Each sentry is the same, so there is no skill curve associated with it. Good players know what it takes to bring down, they know how to coordinate, and medics / ubers are common (I think 2 medics per team is the standard?).Offensive engy can work on a pub, but a soldier / demo / heavy & medic can take down a level 1 or 2 sentry no problem. An engy can't keep up with the flow of 5 CP maps. Teleporters are unnecessary since scouts don't need them and offensive classes stick w/ their medics. Dispensers are less necessary with ample medics are fewer players sharing the ground drops. Now, a pro team does typically field 2 scouts, which would make you think the engy would be useful, but I guess that's not enough utility to offset the drawbacks. I have no idea how valve could make the engy work.
Without engies, the spy is just a backstabber. A small team that talks and sticks together is less likely to be susceptible to a spy.
Without sentries to defend or spies to discover, the pyro becomes pretty much useless, not to mention he gets owned by the other offensive classes. They're also the nuisance class so I can see why pros would have no problem keeping them out of the game.
I don't think there's a way to "fix" TF2 for pro gamers, although a few tweaks couldn't hurt. The classes that aren't played are support classes that don't gain relevance in a 6v6, 5 CP format.