Elminster can also train clerics, fighters, and thieves; later writeups of him gave him a few levels in all the major classes but still not enough to train 39th level clerics. Elminster himself was only a 26th level mage in 1st edition Forgotten Realms, which means even he can't train party mages.
My opinion is that Pools of Darkness is a great game and a pretty good D&D adaptation. DQK is a pretty good game and a pretty good adaptation. The designers couldn't do anything about the fact D&D, particularly 1st ed, breaks down at high levels.
In fact, in 1st ed, once you hit 18th level the gods were supposed to kick you out of Krynn. Guess that would have been a lot less fun for the players though, as you would have only had 4 levels to go after Death Knights of Krynn ended. I think the only trace of this is Knights of the Crown and Sword capping out at 18th level.
A lot of the XP gains in DQoK (and to a lesser extent POD) is 'party gets experience'--I remember getting a few hundred thousand for agreeing to kill some dragons (not killing them, agreeing to) which strikes me as silly.
Basically, they took a gamist (make the game fun) at the expense of simulationist (copy a real game of D&D) approach. Dark Queen of Krynn has covens of 27th level wizards attacking you, and grunt forces in Thenol are 16th level fighters, which basically means they should have conquered the minotaurs and be sailing over the sea to sack Ansalon by now. Granted it makes a little more sense than sticking enough 8th-14th level characters to conquer all of the Forgotten Realms in the middle of a mine (or glacier), but not much. Pools of Darkness kind of had the excuse that only the strongest fighters and wizards would be running around in the post-apocalyptic Realms. But the grunt Zhentil Mages are 10th level or so, and Semmemmon (no. 3 after Manshoon and Fzoul) had only gotten to 12th by 1st ed.
I think one of the other things holding them back was that the standard high-end enemies, the demons and devils, were sort of being downplayed due to the Satanic D&D Panic of the 80s. Bane's lieutenants are t'a'n'a'r'r'r'i, not 'demons'. They also probably didn't have enough left in 640K to program all the spell-like abilities in; Gothmenes should be able to toss uninterruptable fireballs at you (since they used 2nd ed stats for him) like a death knight in addition to swinging his vorpal longsword around.
Another thing (confirmed by a post on TSI's website) is that they were apparently constrained by IP rules at this point; I guess TSR got annoyed at them killing Lord Soth and Kitiara (more or less) in Death Knights of Krynn.
In short, they had the 640K limit, the brokenness of the rules at that level, and late-80s PC and TSR's legal department to deal with, and they still did a pretty good job.