I disagree a bit on this. Although there are a lot more monsters that have spells, I think for the most part they are there for flavor / world building and can be easily ignored on purpose. What I mean by this is that the CR of the monster, unless it is primarily a spellcaster, is not determined by the spells it has. They are there for an extra layer if you want them or need them, but you can run the monster completely fine without them. On top of this, the new standard appears to be to include a relevant spell description in the actions, like
chromatic orb from Auril's first stage:
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I think this is a good compromise. You have a spell you are likely to need stated out for you, and then some flavor spells you can use if you want to, but you don't need to.
I think what they're doing in there (presumably in Frostmaiden?) is good, but it's not how it's been done historically, at least not in a lot of cases.
I don't agree that "for the most part" monster spells are for world-building, certainly not the in the books I own (which is all the actual monster-books and most of the setting books, but not the adventures). On the contrary, by far the majority of monsters which have spells seem pretty reliant on them, and the spells are often poorly called-out. It's not a few monsters, either - it's a large number, and sometimes they have quite an array of spells. You can usually get somewhere by starting at the top of the list, spell-level-wise, but it's a messy, clumsy way to do things, and the balance is dodgy. You say the CR doesn't include the spells - I don't agree - but I would say it's inconsistent. There are some monsters where, if you don't use the spells, they're nowhere near that CR, but there are others where it just appears to be a "bonus". CRs in 5E are generally pretty dodgy, way behind 4E in reliability, but at least they're way, way ahead of 3.XE, where they were actively misleading (as in, you'd get a better result eyeballing stuff than using 3.XE CRs, and two monsters of objectively extremely different power levels could easily have the same CR because of the weird-ass way it was calculated).
This blog can help.
The Monsters Know What They’re Doing - Ready-to-Use Tactics for D&D 5E
Even if you don't agree with his tactics, he explains his reasoning and assumptions, so it's easy to work out your own
I haven't read all his stuff, but I think he falls into the trap of stats = personality pretty often, and often totally fails to account for the mindsets, cultures, and so on of the monsters in the tactics he lists. I think he's representative of the cultural problem D&D has here with this insistence that DMs have to use certain tactics for certain monsters of they're in some way "bad DMs" (some of his pieces very much have that vibe, especially earlier ones). They're full of weird assumptions like that creatures with Darkvision always prefer to fight at night, too, which often make no sense holistically (for example, in situations where most creatures the monsters interact with have Darkvision, there's no advantage, and he seems to forget that even creatures with Darkvision still get Disadvantage on Perception checks in darkness, for example).
All that said, he does go through the abilities/spells a monster has systematically, and whilst his conclusions are almost always a bit metagame-y and facile, he does sometimes come up with some kind of golden idea. Re: explanations, he usually explains, but a lot of his pieces involve so much assumption that he forgets to explain certain things. I'd be cautious of pointing less experienced/confident DMs to his stuff because I think it's such a narrow mindset.