In season 12, episode 24 of the anime, there have been several instances when some Pokemon used the move Hyper Beam, but they didn't have to recharge. For example: (https://drive.google.com/file/d/1NcheLfkMuu8SYovKSQv6nwzB4cOcZnCk/view?usp=drivesdk) In picture 1, Salamence uses Hyper Beam, and the time is 6:13. (https://drive.google.com/file/d/1NoF4PgdJA5V_OXxR7YW_avhiXcBhriTR/view?usp=drivesdk) Salamence uses Hyper Beam again, and the time is 6:15.
Another instance is in these pictures. (https://drive.google.com/file/d/1NsiIP49iuFjBfTuaU_ycY38p48sdPrET/view?usp=drivesdk) (https://drive.google.com/file/d/1NvC8UnJyTe1zmIxTjV69tr4n-5b1PhFi/view?usp=drivesdk) (https://drive.google.com/file/d/1NvEqUFGp45Dnc0Fz_m7Ce_sBsQ4hqI0A/view?usp=drivesdk) The Regis use Hyper Beam several times without recharging. Also, I'm pretty sure the Regis used Hyper Beam more than 5 turns and shouldn't have had the PP to continue using the move. If someone could explain this, that would be great.
I think the anime could not represent Pokemon recharging also not everything in the games are represented perfectly in the anime like charizard learning tackle for example we see a good example of that in the kalos anime when team rocket try to control a salamence it uses Hyper beam consecutively without recharging. Also most Pokemon represented there are seen as ferocious, dangerous,Extremely OP and recharging would make them look more under control and would not help the action .
hope I helped