To me this is trying to go back to the game we knew as a child, where pitchers had to pitch longer. The reason that teams have 1 inning pitchers and LOOGYs is because it works better, you have guys that can come in and throw 97 with wicked stuff for 10 pitches, and you create matchup issues. To me that is "natural" and trying to limit the number of pitchers just tries to impose a rule for a less successful version of the game (although with all the breaks less enjoyable also).
It is better to try and find a way to let managers do what will help them win and shrink the time it takes rather than try and stop them from making moves just because of some artificial/arbitrary rules, because they will find ways around those rules. Just like last year when suddenly every team had a "slush" roster of relievers that were waiting for their fake time in AAA to expire.
If they imposed a 3 hitter minimum I think it would be better than what we have now, but I would rather find a way to shorten games without that rule, which I do think is arbitrary.