There's a pretty straightforward explanation: Language is magic. Some languages are very magic, and either cause or can be caused by magical eddies that are easily perceivable. Lingua Presentia, etc. It makes a lot of sense for those not to drift. Correct and incorrect usage are obviously differentiated. If the effect is strongly reduced with the mundane languages, you could still have the effect that changed words typically just don't feel correct, and so it just doesn't enter general usage. Words would still produce a faint magic echo which can be subconsciously felt, and it should either match the previous word used, the general meaning, or at least not feel dhary. Getting that by accident would be rare. That would massively slow the rate of change.Unless you bring Tolkien back from the dead and convince him to chip in, I'm not going to rewrite the entire linguistic history of the setting. It's not just one example of a head-scratcher, it's baked into the entire thing. Reikspiel and Bretonnian are mutually intelligible, as are Estalian and Tilean, as are all the Elven dialects, despite all of the above having parted ways thousands of years ago. Khazalid hasn't budged a hair despite every Dwarfhold being essentially isolated from each other for millennia. Skeggi still speaks Norscan. Skinks have developed their own dialect of the spoken language of the Slann, and it's all mutually intelligible across two and a half continents. All Beastmen can understand each other. Most greenskins can understand each other, and when they aren't it's about subspecies, not geographic distance. I could go on and on. Completely rebuilding all of that is not inherently the 'duty of quest GMs and fanfic writers', it's a Herculean task.
Of course, I'm not even sure that's necessary. Roman language are often still mutually intelligable to some degree (french and spanish). German and Dutch still are to the point it can be hard to tell whether the other is talking another language or super high (a Dutch would say super drunk, but what do they know, they're always high). That's not the same timespan as in Warhammer, but still a good chunk.
And of course, dwarf languages changing would be more surprising, especially in Quest where Khazalid is definitly tied into the magic of runesmithing, and that might a "correct baseline". Plus Living Ancestors. If your not speaking like the Living Ancestor, you're clearly doing it wrong.