The loser can't get any less of a CP than they could from the ban-system, it's just that tthe winner can't get screwed over as hard. We want skill to be tested during a match, not on a menu. The main principles behind the pool-system (besides being faster) is that it selects a stage with which both players are content in a manner that is minimally abusable - increasing player satisfaction and perceived validity of the results - while also being more feasible and allowing more variety than FLSS'ing every match.
Here are some example scenarios, in which we suppose Player 1 won match one, Player 2 lost, and neither switches character:
If P1 is fine with Halberd, there's no problem if they play there, so suppose P1 isn't.
Ban-system: P1 might assume P2 also isn't, and so he bans some other stages; if P2 chooses Halberd, then P1 feels cheated, blames the stage if he loses, and demands that it be removed from the stagelist so that such cannot happen again. Alternatively, P1 might predict such a scenario, and so he bans Halberd every time; if P2 doesn't care for Halberd either, then P1 effectively has n-1 bans when the rules intend him to have n, and so, realizing this, he demands that Halberd be removed from the stagelist so that he's not disadvantaged.
Pool-system: If P2 dislikes Halberd, then she just doesn't pool it. Suppose P2 does like Halberd, so she pools it along with n other stages she also likes. P1 now has a choice among n+1 stages, as intended by the rules. If he doesn't pick Halberd, then Halberd is no different than the rest of the unchosen pool. If he picks Halberd, then there are at least n stages he prefers it over. Regardless, removing a stage from the list would require more substantive reasoning than personal preference.
The idea here isn't to
force players to use stages they don't care for; in fact, we specifically want to avoid that, as it's what gets the stages removed. Rather, the idea is to
allow players to play on stages they both think are relatively fair.
Ban-system: P1 bans FD and some other stage(s), then loses. P2 doesn't want to play on FD, and may infer that P1 doesn't either, so she doesn't use a ban on it. If she's correct, then she effectively has the advantage of an extra ban (or more, up to double the norm). If P1 does choose FD, then P2 feels cheated, since she could have banned it. Either outcome is an unintended abuse of the rules that devalues the actual game.
Pool-system: P2 pools FD and some other stages, then wins. P1 wants to play on FD, and may infer that P2 also does. That probably wouldn't change P1's opinion of FD, and any stage he might pool instead of it could also be the next stage P2 would have pooled. Ultimately, it's not worth gaming the system, so players might as well just use it as intended and focus on the matches themselves.
Accounting for non-hierarchical stage preference makes no difference here. The pool-system is based on choosing stages that you want to play on, which is much easier to figure out and far less likely to change when given new information than the ban-system's basis of barring stages that you think your opponent wants to play on. Consequently, the former is more intuitive in application and resistant to exploitation.
P1 doesn't want to go to Lylat, but isn't sure if it's in this tourney's stagelist.
Ban-system: It's in P2's interest to say it is, whatever the truth: she can't choose it regardless, but saying it is means 1 less ban from P1. Hence it's in P1's interest to check the official rules, which slows things down. He could just reveal what he'd ban instead to find out if it matters to P2, but that's some important information (see previous example).
Pool-system: If P2 doesn't want to play on Lylat, then it doesn't matter. If she does, then it still might be that P1's #1 choice of stage is already in the pool, in which case it still doesn't matter. If it isn't, then P2 wouldn't be giving up much by revealing what she'd pool instead.
This one may seem trivial, but it illustrates how a system based on mutual comfort just makes things in general run smoother. And in my experience, between experimental stagelists/stages, varying standards across locations, and apathetic TO's that don't know/care enough about PM to make official rules, this situation isn't too uncommon.
The ban-system is functional, but it's not optimal. Pooling is a much more effective, efficient method for Project M, or any competitive game in the genre that wishes to have a sizable list of diverse stages.