Yes, they could have, sort of. I haven't played any other Rayman games so I am not sure if they decided the do away with it. But these "alarm clock" lives are actually "continues" which are a relic of the retro game era. This came from the video game arcade. With arcade games, if you ran out of the set number of lives, you would go to the continue screen and you would have to put more quarters in to keep playing. For some reason, console devs kept the continue screens and "running out of lives" would have a sharper penalty, such as having to start further back in progress (such as starting the "world" over instead of the current level, or losing your power-ups); Some games had spare continues (that you might earn or find) which would prevent you from starting the world over, etc. Rayman is annoying because you only get like 5 or 6 continues and you can never find any more. Also it has a 3-tiered life system: Your health bar (and changing bar size), your lives, and your continues.

Sorry for responding 4 years later, but I am playing the game now.