I think an aspect of combat P5 fails to communicate is that the point is not to just mindlessly exploit elemental weaknesses at all, that's only supposed to apply to mobs where your goal is to win as fast as possible because they can kill you with ease if you ley them act... On hard that is.
Boss battles are more about planning carefully and making use of your strongest moves while keeping buffs and debuffs on to make sure you can survive. Giving bosses weakness would make them pushovers, unless they went the SMT4 Apocalypse and make everything a boss gauntlet, which judging by the reception of a certain moment in Palace 7, people don't seem to like (I love those).
But yeah I think combat only realizes its full potential on hard, and it's a pity this wasn't the default difficulty because it's so much fun. Of course it's hard to say something like that without coming off as pretentious or elitist, but eh what can you do. Normal is simply too easy and you deal too much damage to need to care about strategy most of the time.
The problem with palaces and their length/pacing comes from the fact the developers clearly don't intend the player to clear the whole thing in one marathon. If you did 1-2 safe rooms a trip and visited the palace 2-4 times during the month that wouldn't be an issue. Of course doing this creates the conflict of wasting precious social time constantly being in palaces. I think it's telling that the dungeons that have forced exits due to needing to change cognition aren't the ones people generally complain about, yet that issue ties into the general complaint that the game "waste your time" with so many story scenes where you can't do social stuff.
I really can't even think of a good suggestion to fix the issue as long as persona keeps the format it's had since p3.
I agree, I think the game is clear enough in how palaces shouldn't be cleared in one go, except that they made the terrible mistake of tying the SP adhesives to one of the first Confidants you have access to, and thus making them relatively easily available, so players will bypass the low SP barrier with ease, thinking this is the way the palaces are intended to be played.
I personally don't get the general anxiety over losing days that could be spent ranking up social links, simply because I see the dungeons as the meat of the game, and the social aspects as appetizers... HOWEVER I can see how the many sections that take control away from the player could make this anxiety worse.
And I agree that it's really hard to think of a solution with the current framework unless they were to force you out of every dungeon, which goes against the appeal of time management. And clearly making them shorter isn't an option for me haha.