In an ideal world a no restriction, no class limit based format would certainly create lots of innovation and new strategies and make competitive play more appealing to beginners.
However, in the state the game is currently at (and will realistically stay in for probably eternity because Valve lol), it's not really feasible.
Unless MAYOR weapon and class rebalancing takes place, you can't really convince me that a game where people can run 5 heavies versus 5 engis is more fun to watch or play for anyone nor that it would be less "stagnant" or "slow paced".
I do think that the fact we essentially only play 5CP does exacerbate this, and that other gamemodes might very well develop completely different flows, but it seems there aren't enough maps (being made) to really support this. Naturally, it has also pretty much become consensus that 5CP is, on average, probably still the most fast paced, maybe tied with KOTH, depending on the map.
It honestly just boils down to both how willing people are to stray from what has been established for over a decade, because, if you think about it, there's definitely a reason as to WHY something stays a certain way for a long time.
The same ideas that would bring us some great strats that people could experiment with would in turn immediately develop their own metagame.
People (especially outside of competitive) like to call the current meta "stale", yet do not understand that if there were absolutely no restrictions the meta would simply shift to something most people wouldn't consider any better (Vacc meds, several heavies, 5 scouts, who knows).
Again, ideally, ANY strategy would have a working counter strategy, but as is the nature of class-based games, achieving such balance is nigh impossible.