Power-wise, they count. I actually think even Z-Moves are relatively consistent in how they scale to each Pokemon's power. Taking someone like Lillie for example, the main reason her Z-Move couldn't beat Gladion was because Gladion was far stronger anyway. Or even comparing Kiawe vs Brock to Ash vs Misty, Turtonator naturally scaled lower than Pikachu, so it makes sense that Ash's Z-Move was able to beat a Mega while Kiawe's couldn't.
Even with Pikachu vs Tapu Koko, keep in mind it was a special Z-Move overpowering another special Z-Move. I think Pikachu would've won even without the recharge, it's just that a huge Z-Move clash was way more appropriate for le epic finale.
The bigger problem for me is how overused they are narratively as a crutch. 90% of gimmicks in the anime are treated like the battle's entire worth. Anything a Mega does in base form, for instance, is always written like it's irrelevant when the battle is always gonna come down to how broken the Mega is. Like, it's annoyingly obvious against Alain that Ash-Greninja could've swept through everything other than Charizard, and vice versa. The rest of the battle doesn't even matter when they would've eventually been Mega fodder anyway.
Surprisingly SM was kinda better in that regard, at least occasionally, at showing that Z-Moves aren't the absolute be-all-end-all for everything and should be used strategically. Even something like Infernape's Blaze had natural drawbacks that forced more strategy instead of having this instant super mode that could've been used turn 1 and trivialized everything.