And here's my problem with that: That seems like a lot of steps to do the same thing a regular DC difficulty roll does, but with more steps and less clarity. It really feels like the Trolls' house rules that they love and have never really interrogated.
I agree with you here. The way they explain it in the books is so confusing. I've brought up it up multiple times on the forums and Discord, but there doesn't seem to be any intrest from the Trolls or the fans to change anything.
Honestly the math is fine, I think it just needs to be explained better. I understand some of the reason why though, because as soon as you start nailing things down, it kind of begins to tie it to a specific system, where as they want to keep it as compatible as possible.
What advantage does SIEGE (which isn't actually an acronym) have over a standard D20 roll system?
First off, d20 systems expect you to roll
a lot. C&C is narrating with common sense as much as possible and only rolling when you're unsure of outcome and it's relevant (How 5E should be played too, but some folks love to roll those 20s

). Like 90% of the time you should just be playing it like AD&D, but for the instances you really wish AD&D had skill rolls... that's when you use SIEGE. I prefer this since it makes the game go faster and avoids constant goofy skill scenarios (like 5E can get).
As for mathematical factors, it adds a couple. One is saves/checks are harder to make, especially with Non-Prime stats. The default assumption is if you're rolling you'll probably
wont make it, but maybe luck is on your side... This makes monsters and spell casters scarier.
The second is it puts more importance on Level. Because the difficulty is determined by the difference in Level/HD, every level counts that much more. This is similar to most d20 games, but is nice change from AD&D's system where at higher levels you can make just about any save.
The biggest advantage though? It is so easy to tweak to your liking. You like DCs? Cool, write them in. DC 15 = CL 0, each DC +/- 5 changes the CL by 3. Think making checks is too hard? Change the Target Number (TN) from 18 to 15. Hate SIEGE? Take it out and import Saves and Thief Skills from another system and you still have a great OSR game. Bring them in and give characters a +2 if "skilled". Too much fun, and that not even scratching the surface of the many options in the CGK (DMG) like Spell Points, no Hit Points, "Feats", etc.
Personally I use Prime, Secondary, and Non-Prime stats (+6, +3, +0 bonus respectively). TN lowers 1 every other level. Advantage/Disadvantage from 5E for when it makes sense.
Oh, not as important, but worth mentioning: you can actually roll stats in order! Since most ranges just give you a modest bonus/penalty, the Prime bonus is much more important. This means you can have a completely randomly characters with "average" stats that are still viable.