I think it'd be interesting, but there is no way in any reality Game Freak have or would have the capability to pull something like that off. Anime-style Pokemon battles would probably wouldn't be as satisfying as they sound - although the two Attack on Titan PS4 titles capture the anime perfectly, so who knows? - but I have always found real-time combat in games more involving than turn-based and I think it'd be a welcome and refreshing change of pace. We are looooong overdue a Pokemon Warriors title, and whilst the roster would need to be smaller and no doubt would be filled with crappy popular Pokemon, the gameplay would make up for it if the right people handle it.
That said, how it would evolve would determine if it was better or worse than what they've got...the thing about turn-based combat is that it's very safe. Any idiot can make a turn-based system work, and it's a lot more accessible to people, because not everyone has the reaction time necessary to play games with real-time combat, and learning attack patterns can only get you so far sometimes...contrary to what every elitist Soulsborne fan thinks. There is a lot that can go wrong with real-time combat too - the movement needs to feel right, the camera needs to not get in the way, and it needs to be responsive. If you want an example of a clusterfuck, look at pretty much any Kingdom Hearts title: the movement is janky as hell, executing commands is awkward, and the camera is a nightmare. Compare this with Monster Hunter, which combo attacks are executed with buttons and items are used from a menu, and it feels a lot more fluid and natural. With more than one character the best example I can think of would be the Tales titles, where you can "pause" the action to switch between characters and/or give them commands...although FFXII's Gambit system was years ahead of its time and would be the perfect solution for real-time double battles where, presumably, your second Pokemon would act independently unless you were controlling it yourself.
Outside of double battles, I imagine the best way to handle Pokemon battles would have them in a similar style to a Warriors title...or better yet, Dissidia. The Dissidia PSP titles remain the best one-on-one real-time combat games I've played. Dragonball Xenoverse would be a close second but flying around can make things a bit chaotic...and I shudder to imagine what a battle with a flying-type Pokemon would be like if you were on the ground - it'd probably be similar to FFVII Remake, which goes to hell the second you have to fight a flying enemy. This would cause all sorts of problems with the game balance, and the games could either be a lot easier or frustratingly unfair: real-time combat lets you dodge. So you could either never get hit, or find it impossible to land a hit on your opponent. Maybe that would please some as it would necessitate difficulty settings, but that doesn't guarantee a balanced system. I mean...what would they do about special moves? The PP system wouldn't really work with real-time combat. I suppose a tried-and-true MP system could work, with stronger attacks requiring more MP to use (it's worked well enough for the Tales series) but then, they'd need to design regular attacks for every single Pokemon.
There are too many things involved with real-time combat for it to go wrong with something like Pokemon, honestly. I think it'd be amazing if they had a one-on-one Dissidia-style system with button-based special moves (e.g. press X to use Flamethrower) and an MP gauge that recharges over time/the more you hit an opponent, and if they utilised FFXII's Gambit system (I'm sorry, but that's better than just telling your AI to "Attack weaker enemies!" or "Focus on healing!") in double battles so you could rely on the Pokemon you weren't controlling to not make phenomenally stupid choices (bad AI is the biggest curse of every JRPG with real-time combat tbh) it could work, but I have no idea how to best get around fighting flying enemies on the ground without it dissolving into a complete mess...not every Pokemon has a ranged attack, and if dodging is going to be a thing - which is kinda needs to be really - then...yeah. Nah.
So yeah, potential to be better, but Game Freak definitely do not have the ability to do it. There's always Pokemon Rumble I guess?