Then how about I bring 5 different cues with me with different diameter and materials, also different tips and weights of cues. Lets say I come to the pool table with one CF shafted cue and 4 other wooden cue, one is 12.5mm and one is 12.2mm and two with hard tips. Another cue I bring that is 17 oz weight and another that is 21 oz weight.
Then with each shot I choose different cue for certain shots? do you think that should be allowed too? based on your argument it should be allowed. Maybe I use the heavy cue for hard draw shots, then the light cue for the slow-roll shots.
Since you think golf is the same as pool, lets also do this? I'll send a letter for the pool-society maybe they approve.
In more seriousness, I hope you can see that issue here. Golf is not similar to pool. Playing on a small table is different than playing on different grounds/ large field/ different elevations etc.
I have no issue with someone bringing 15 cues if they really want frankly, if someone wants to play as you propose and can do so within the time limit (assuming there is a shot clock), I'd have absolutely no issue with that (although I'm not convinced it would be great viewing).
That said, I still consider it the same, golf has a limit of 14 (I think) clubs because the courses are bigger with various hazards.
Pool has a limit of 3 or 4 (I'm assuming there actually, not actually sure if that's true, or whether you could theoretically bring more), but lets say most players probably have 3 (plus perhaps spare shafts). They then use a break cue (driver) to break (tee off), they then use a playing cue (3 iron) to play (hit off the fair way) and then a jump cue (sand wedge) to jump (i.e. when stuck in a bunker).
To be honest the more this goes on, the more similar I think it is!
Obviously, joking aside of course the games are vastly different, I just mean that the concepts are actually pretty similar and saying having 15 cues (or whatever) might well be ridiculous, but a limit can still be set and if its not already 3 cues, then why not just formalise this.