Yes, I agree that the rules are terse, and sometimes needlessly so. That is somewhat offset by the plethora of play aids, tutorials, and youtube videos.
There are several things I like about ASL. One is the modularity. Once you learn the rules, it opens up thousands of scenarios, each telling a different story -- and there are stories within the stories when you actually play. I also think the rules also a lot of tactical freeplay, which is sort of surprising considering how thick the rulebook is. The dice can and they can not play a big role. There are a lot of things that you want to do but won't be able to do because you failed a roll, or your machine gun will break. The scale of the game is also wonderful - I can feel like I'm down with the squads trying to cross the street into the village.
I won't say ASL is the best. I think other systems have learned from ASL, and taken the good elements without all the chrome. The starter kits are an example - they have captured 75 percent of the game with only 50 percent of the rules. SK1 is a bargain, not that difficult, and people are producing a lot of SK1 only scenarios.
I highly recommend Jay Richardson's tutorials. Highly recommend. The pandemic has also pushed me to get VASL running, and now I love it. I have a small network of friends that I'm helping learn through the starter kits. Let me know if you want to join us sometime.