Why can't we have both. Golf has plenty of tournaments that are both handicapped and open. Pool can have the same thing. It's not going to breed mediocrity. It's going to give some casual players a chance to compete with better players without having to put in years of blood and sweat. No one is going to sit around and think, "hey, I'm not going to try to get any better at this game so I have a better chance to win that tournament." I can tell you, that certainly isn't how the players feel in golf. Not trying to improve doesn't give a better chance of success anyway.
Bowling is another example of handicaps not breeding mediocrity among the players. I've have bowled in several leagues, and I have never met anyone that did not want to improve and lower their handicap.
Now basing player handicaps on their league rating may not be fair, depending on how many different leagues are represented, or if the league's rating system is flawed. I have never played a handicap league, so this is just anecdotal evidence, but the main reason I hear for people sandbagging in pool is because of the max team rating rule that causes teams to have to split up. Again, I am not claiming that is gospel, just that it is what I hear most about here on AZB.
I prefer no handicap when playing, but that is just my personal preference. I am (gasp!) liberal enough to accommodate all types of play in this sport that I love.