The American system works (to some extent) because it's conducive to the structure of the game (i.e. punctuated by a succession of stops and commerical breaks). It also works because managing timeouts are a key part of game strategy, and coaches don't want to risk losing them.
Most importantly, however, it works because *every* professional game that is played is covered about 20 cameras that cover every possible angle of every play
Even then, this is the second time around for instant replays in the NFL - the coaches hated it so much the first time around that they scrapped it. This time around they severely restricted it.
And for all that, just watch any random game on a Sunday afternoon and I guarantee you will see the commentators point out at least half a dozen bad calls made by the squad of officials - often ones that can have a big impact on the game. Case in point yesterday, the Cowboys punt returner that stepped out of bounds on his way to 97 yard touchdown run.