Arbitrary because they are largely made up by the LOs, and are very subjective to the small area the league happens to be in.
A 5 in one area might be a 3 or a 7 in another part of the country.
There's a system out there now called Fargorate that tracks and compares every single person in the system, world wide. Eventually almost everyone will be connected, and the ratings become very accurate over time. (starter ratings can be a bit arbitrary, but they correct themselves)
Stated just like those who insisted the world was flat, because they did not know better. APA skill levels are largely objective, based on data from the scoresheets, with a little subjectivity added in. Like I said before, variances depend on the diligence of the scorekeeping (objectivity) and the diligence of the LO (subjectivity). I challenge you to give me the name of ONE person and TWO areas where that person is a 3 in one area and a 7 in the other (with plenty of scores in both). Someone who isn't cheating. If you can do that, I'll show you which of those two factors has failed (likely a combination of both). But I bet you can't. The response to that challenge is usually something like "Well, I don't personally know any but I've been told they exist." Maybe you could 20 years ago, but not now. 3 and 5? 5 and 7? I'm sure you can do that, but those numbers are just one skill level apart (the best 3 and the worst 4 are essentially the same person, as are the best 4 and the worst 5, so you end up with the range of the SL 4 in between).
The subjectivity part is necessary, as the creators of the FargoRate system are finding out. That's because a computer model of actual ability cannot ever be 100% accurate, and is the easiest to cheat. There has to be oversight. Never mind that comparing FargoRate with the Equalizer is a flawed comparison to begin with (the two are designed for different purposes), both systems have to be watched closely to protect against the flaws introduced by primarily being objective. And contrary to popular belief, there is cross-pollination in the APA system too, primarily in the subjective part for now but eventually in the objective part, too.