As the Librarian and other scholars on Lovecraftian fiction have said ... they're all just plot tools.
The people who came behind tried to create a "Mythos" from it all, and DID create a "Mythos" from it, but use it as you may.
Magic in those stories is, likewise, a plot tool. I don't think Lovecraft really made some sort of choice to "limit" or "expand" his use of magic in any story or whether or not to mix "magic and The Old Ones" in any particular story. He had a story to tell, he got it across in his way.
The "Arkam Cycle", the common names, themes, the "mythos" was a flavor element. You have to think about where his body of work appeared ... shorts in literary magazines, serialized in places. You read half a dozen "Fantastic" or "Horrific" tales and what stands out? Recurring names and themes, for one. Yog-Sothoth, the Necronomicon, etc etc. It made him stand out a bit, for one, and made for a handy hat to stick on a hook.
CoC as a game is, first and foremost, a game. It's different for everybody. So some people like different things.
I think, for the original poster, what would be a more effective exploration would be ... what spells, for you, serve the same effect as those spells served for Lovecraft?
You'll notice they were all plot devices. "Summon Yog-Sothoth" "Banish" ... Trap The Soul, a defense against Trap The Soul.
Just using these spells willy-nilly will as much bugger the feeling of Lovecraft's fiction as letting the character run about casting Fireball.
I'm not going to use magic and Tomes as: "You find a tome, you lose Sanity, *roll* it has 4 spells, *flip flip flip* the spells are _______" ... that, to me, would ruin the whole INTENT of the game.
The introduction of magic should have REASON. You don't find Dust of Ibn Gazi. You're told about it and given it by the crusty old half-mad sage and you use it on the invisible horror you'd normally have been unable to even SEE.
Non-"core mythos" spells can be introduced and still develop a lovecraft "feel". They just need to be present as plot hooks and very very rare. Specific spells introduced to combat or counter certain enemies. And never let the spells of the enemy fall into the hands of players unless they'll need the two-edged sword of magic to combat a very specific threat you've set up for later in the campaign.
--fje