Or it's about money for the university degree they know the kid wants but can't afford. There's all sorts of angles and I would guess they have a standard pitch based on score, location, estimated socioeconomic background.

I mean. At least that's what I would do if I were in charge of recruitment.

That's actually what I'm thinking, too. "Oh, you scored between this bracket? Your code name is 'Meat Shield #1947288'. No, it doesn't mean anything. Stop asking. Now get out there champ. Make 'em proud."

I'm old enough that we didn't really have those technical things when I would have been enlisting (early 90s). But even then I remember our guidance counselor telling us, "You'll get 5 calls. One from each branch, all asking you to enlist. You can just say no."

We all took the ASVAB, as I recall - it replaced a class period. For some reason, I remember the room I took it in, so I'm pretty certain it replaced a language class (German, in my case - it was a small, windowless room, though I did have a study hall in the same room one year). When I met one on one with the guidance counselor, he looked at the ASVAB and said, "Well, you're qualified for every job in the military, but you're probably not interested." Then we talked about other careers and college.

Now that I think about it, that dude did me a world of good on several occasions. I wish I could find him and thank him.

Hilariously the Infantry isn't where the really low scores usually end up. You actually need to be a certain kind of smart to do that.

The score matters as far as what jobs you qualify for, and it also tests different aptitudes. For example, two people could have the same overall score (say a 70), but one person could show mechanical aptitude and be pushed toward a Machinist position, while the other could do poorly on mechanical but do well in electrical stuff and become an electrician.
They also don't want to waste their smarter people as basic grunts or cooks, so a higher ASVAB score can mean you're less likely to get the job you want if, say, you score 90+, but always wanted to be a chef. If you have a specific job you want to go in for, you basically have to get it in writing that you're joining for that job, otherwise you're at the mercy of the "needs of the {branch name}" - you will be what they need most that you're very good at.