Since I've been thinking about Gust RPGs lately, Atelier Iris 2 and 3 ditched MP in favor of a team power gauge. It worked more like TP, starting from zero, and going up as you do damage and combos and such. All characters charge and consume the same bar. So you might have all of your party members wailing away at monsters for a few turns so that one character can charge up a super attack that consumes 3 levels of power gauge. Yanfly has a plugin for this:
http://yanfly.moe/2016/02/06/yep-67-party-limit-gauge/
The main con for this system is that it only really works if you are fighting a powerful opponent. If you are fighting enemies that go down in 1 or 2 hits, you're not going to charge your bar at all. The Atelier Iris games addressed this by throwing insanely fierce monsters at you all of the time. But this means that after a certain point, every monster encounter is like a boss battle, and the later levels can get very time consuming. And it's more of a strain on the developer to come up with genuinely difficult encounters all the time. Another con is that it puts more limitations on your skill-use resources, so you tend to stick to a favorites instead of using every single skill at your disposal. So you end up with one character using skills, and all the other characters boosting the gauge.
The pro for this system is that it's more strategic than using MP, and it's more rewarding to use skills since you have to work to charge them up. Actually, a lot like Limit Breaks. I guess it's like if you just used Limit Breaks for everything instead of MP.
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Final Fantasy 8 also skipped MP, but people tend to give it grief for doing so. Magic works like items. When you use a Fire spell, it's gone, you can't charge it back up at the Pokemon Center, but you can Draw more Fire spells from Draw Points or firey monsters. (and deeper in the game, there are various ways to get more magic) You could also junction spells to your stats. So for example, you might junction Fire to your ATK stat. So each Fire Spell would raise ATK by 0.2, so if you have 50 Fire spells, you've got +10 ATK. But if you cast Fire while it's junctioned, you're going to eventually reduce your ATK stat. And while normal magic worked like that, GFs (Summon Magic) could be cast for free, and using GFs would increase their GF levels and make them do more damage. The only catch was that GFs took longer to cast, and GFs could take damage while being summoned, but this was sorta offset because summoning GFs more would increase their summoning speed. FF8 also had the ability to use Limit Breaks infinitely, so if you could set that up, Limit Breaks were usually automatically better than Magic, although I think Irvine's consumed items and Rinoa and Selphie consumed magic for theirs.
So in practice, there was almost never any reason to cast any sort of Magic, except for a few staples like Cure, Esuna and Aura, and even then, generally better to junction them. This was especially true as you got into the end-game spells, Flare, Meteor, Holy and Ultima. But it also meant that spells which are usually useless like Demi and Shell could still be useful as junctions. And the GFs were interesting enough that doing nothing but summon GFs could still be fun, but I think they could have done more with GFs if they had realized that there was no reason to use the rest of the battle system.
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It also surprised me to learn that the original RPG, Dungeons and Dragons does not use MP. D&D uses the concept of spells-per-day. So you might be able to prepare 5x lvl1 spells, 3x lvl2 spells and 1x lvl3 spell in one day. Wizards would have to prepare specific spells, so you might say, okay, today I'm going to prepare 3 Magic Missiles, 1 Speak with Animals and 1 Exploding Runes. Sorcerers would be able to use their spells-per-day to cast any spell they know, but they don't know as many spells as Wizards do. Fun Fact, Final Fantasy 1 also borrowed this system from D&D, instead of MP.
Cons: this system struck me as incredibly tedious to set up. I would be constantly second guessing my magic choices and wondering if it were the right time to use my only Speak with Animals spell of the day or if I should save it for something later. I never liked this idea, and it has kept me from ever even wanting to play a magic user in D&D. I guess it's less math than counting MP for table top games, but it feels like the alternative would be so much more complicated. But I will say that a spells-per-day mechanic would make more sense if you were something like a mad scientist inventor or alchemist, where the spells per day represents gadgets or potions or something that the character is crafting on the fly.