While having a replay system is a nice feature, it is in no ways a necessity for competitive play. In fact, many top gamers at the professional level, i.e. make their living playing games like Starcraft, have advocated that a replay system has diminished the competitive field because so many people can just copy their strategies or see how they play.
Starcraft didn't have a replay system when the game first came out either. It was patched in at a later time.
No, it's not needed but it is a big part of competitive play. Those top-star players are complaining about a long and ancient problem that's hardly limited to the pro gaming world and has little to do with replays specifically.
The same problem lives in magic the gathering, for example, where there are no replays (correction: aside from a few tournies). You will always get crappy players who can't think for themselves, but that's not part of this problem. The replay system encourages competitve play the same way it does for nearly every other competitve event, such as football.
Teams watch replays to see where they did poory and where they can improve and to see why another team was so effective against them. It's an incredible tool used by many pro teams, I'm surprised if most pro-starcraft teams really say that as replays are really popular in Korea for starcraft and I watch plenty of them from tournaments.
I myslf always keep a stock of them to see how I screwed up or why a particular strat. works so well against me and that helps me improve. That's completly different from just watching good players and simply copying them. That's simply something you can't get away from, "cookie cutter" is the name of the game, and you find it freaking everywhere. Cookie cutter builds in WoW, FFXI, the "best" builds in old school rpg's, the "best" (cookie cutter, in other words) builds in DotA., ect.