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In our PF1 games we have been using what I think is the Arcanist system under discussion (we call it "Diamond Throne" as that's where we picked it up).
I started reading this post and was going to chime in and say it sounds just like the system we use. Gee, I wonder why it sounds so familiar?
It goes without saying that I'm fond of this house rule.
Someone mentioned flat checks and now I'm playing with the idea of all casters having one special slot per spell level that can be used to spontaneously cast any spell of that level, but it locks once utilized. By spending actions to focus (flavored by the type of caster - recall the fleeting arcane words, call upon your deity's grace, recapture the harmony of the eternal symphony, ask a stick for a favor), you can make a flat check to unlock one of these slots, the difficulty of which depending on how many actions are taken that round-
One action: DC 20 flat check
Two actions: DC 15 flat check
Three actions: DC 10 flat check
Success unlocks a single spell slot of your choosing, allowing you to use that slot to cast another spell with no limitations on number of times per day (beyond that of material component expenditure, for spells with nontrivial components).
Something like that could be an interesting variant on the system, giving casters a bit more freedom to expend spells in or outside of combat without being able to spam magic endlessly (because chances are the best you can average is a little better than one spell every other turn).
EDIT: And now that I look at it more closely, I misread the proposed system and basically suggested the same thing just in more explicit 2E terms. XD Oops.