I have played in AL games, and have run AL adventures (but in the latter case not as AL games). I DM professionally and the main reason I don’t run AL is that I don’t encounter demand for it. It would be a case of me having to introduce it to players, many of whom are completely new or new to 5E, and having to explain an additional set of rules and restrictions that in some cases contradict what DNDBEYOND is telling them (DNDBEYOND, the main tool we use for character building and campaign management, has no AL integration).
I wonder if this is partly regional? In the NYC area, D&D is extremely popular but there are very few game stores and the ones we have don’t seem to use AL. Also, the NYC area has no large conventions. But there seem to be places where AL is a big deal?
Ran a lot of AL at a nearby flgs precovid & can confirm the same experience. AL is good for getting people in the door, but any gm with even a modicum of skill & stability is likely to develop a stable group unless steps are taken to avoid such a thing like randomly assigning players to gms or similar nonsense. The stable group doesn't usually give a fig if the game is strict AL legal & someone looking to find a game who shows up with an AL legal looking character doesn't likely care much either.
The only exception that seem to care about how strictly AL legal it is right down to
"what's your dci number?" type stuff are problem players that bizarrely present a lot like " commercial gold farmers" in mmos who tended to abuse the fairness things built into AL loot distribution exactly like you'd expect "gold farmers" to do in an mmo until wotc redid the AL rules to make treasure more like a point buy thing.
The "log sheets" were a well meaning but misguided idea though. A newbie joining might zealously fill them out for a while until realizing that nobody cares much. Unless it says GMbob gave out a holy avenger & bob is across the room running another table to say "hey gmbob did you give out a holy avenger to a level 5 pc a month ago? wtf?" it's not like the log sheet tells me anything useful when I could just look at the character sheet & say "yea this all is cool but ixnay on the holy avenger if you want to join my level 5 group".
Those log sheets are even worse for not actually being anything notelike about the session. If a player came to me with five levels of session notes filled with things like npc/place names details plot hooks etc & things like
this I don't care if every page was forged that very day because if it keeps up once they are at my table I'll feel like I won the freaking lottery with that player