The reason time saving is more important for pros is because they have many matches to play. Leagues, even without this rule - will still finish.
Pros will not abuse this tactic, they'll use it when the situation presents itself as the best option (the way it should be). Amateurs, especially the types of people you see in the APA, will abuse this and make it their sole strategy for winning the match.
Every team will have their SL2's and SL3's coached to 3-foul the other teams' SL2 or SL3 or maybe even higher! You think this isn't possible? Look at some SL2's and SL3's who take 10-14 innings to finish a rack. When one of them gives up ball in hand - they're on ONE foul. 2 coaches after that could coach for 2 more fouls pretty easily.
It would be highly stupid.
IN FACT, it would waste MORE time...since the lousy SL2's and SL3's would be wasting time trying to attempt a 3-foul attack only to have it fail because they didn't hide the cue ball on the last safety attempt, or the other player gets a hit. That would be even more aweful.
All I know is, you add that to a league like the APA, and I guarantee you that people will be trying it way more than the pros do - and will waste more time in the long run as well as change the nature of the game.
Edited to add: also, the APA for example, is a league designed to please low-handicapped players and has cry-baby rules built in. When SL5's and SL6's 3-foul lower players over and over - the lower players are going to quit the league in frustration. They will resent rules like these were they lose like that. It's just like the balls on the break rule. Make a solid - you have to play solids. Make 1-1, open. Stupid rule. I know the vast majority of rules in the APA are geared for bar-tables and that type of environment. However, that rule puzzles me to this day. It isn't a real time saver since most people don't agonize over group selection. It has to do with the psyche of low level players. Low level ball bangers HATE IT when they make 2 balls on the break of one group and fail to "win" the group only to have their oppenents take it. Thus, the cry-baby rule. You get what you make and that's that. It also slows down the higher level players advantage in being able to pick the better groups. If you haven't seen this, play with true bar table players and see for yourself. These types of players feel there is an entitlement to having the group in which they make the most balls or a ball.
Same thing with jump cues. Ball bangers often just buy a bud-light $30 cue and soft case and play in traveling bar leagues. If you break out a jump cue, you are introducing a new piece of equipment to the game that the other player isn't likely to have. If they allowed jump cues, it would be a defacto way of saying to everyone that to play in the APA fairly, you have to buy "extra equipment" and the APA doesn't want their players getting that message...not to mention, hardly anyone can jump in that league (so it favors the better players).