Let me rephrase that a little bit. If we limit ourselves to correctly assembled cartridges, having an azimuth adjustment on a tonearm is a disadvantage. It can only introduce an error where there was none.
And there's a second corollary. In a correctly designed and adjusted playback system, the only source of static azimuth error is imprecision in cartridge assembly.
And this is probably the reason why, in the otherwise encyclopaedic AES Disk Recording Anthology
, azimuth is only mentioned a few times, and always in connection with cutting, rather than playback, of LPs. It was considered a solved problem: "Why, you just build your cartridges correctly, and that's it!"
Unfortunately, nowadays it isn't so. While most mass-market manufacturers have decent quality control (for example, I've never ever had to adjust azimuth on an Audio Technica cartridge), smaller operations probably lack the necessary tools and expertise to make sure the cartridge is assembled correctly. Azimuth (and SRA) errors of 10° are not unheard of.