Problems with 3cp compared with 5cp.
In 5cp (at least in comp), rounds are generally divided up into 3rds: 1/3 is spent fighting at mid (midfights, and transitions), 1/3 is spent fighting on the second point (after a team loses a mid or fails a last push), and 1/3 is spent fighting on last (the last push, in which defending teams are turtling HARD and trying desperately not to lose a round).
All three of those modes of play are fun and interesting, but as much as possible you want to avoid a team being put into a position where they defend the last point for many minutes at a time, because defending last is a GRIND like no other. The defending team sits it out and goes crazy with defensive shit (sentries, pyros, snipers, heavies, etc) while the attacking team sits back and builds uber, afraid to poke there head in case they lose a med or a key player before a push (thus allowing the enemy team to get uber in time defending the next push).
The problem with 3cp is that as soon as a team captures a middle point, the entire rest of the round is a last defense. Either team is put into a position of being forced to hold out on the last point and prevent a single player from capping it and losing the round, and the other team is put in a position of having to deal with the massive turtely defense of the other team. Instead of it being 3rds, it becomes a 1/10 to 9/10 split, where you spend a minute or so for the mid fight, and then get locked into last defense for the rest of the round.