You do realise all the other God of War games were the same when it came to executions, right? And by the way, the "attack" is actually called "Executioner's Cleave", and based on how they're performed (With the camera moving in for a good cinematic look), I'd say it's safe to call it an execution. (And it seems some people on the internet agree)
Also I put 42 hours into the game during my playthrough, and not once did I see this as a problem.
Yes, of course I realize that the previous games had one execution for enemies too. But it's 2018. It's PS4. It's next gen. Are we supposed to be ok with old, lazy mechanics up to now? That's like saying we can forgive games like mass effect andromeda for having last gen facial animations.
And no, sorry, but the R2 axe move isn't an execution. It's an attack. You can do it anytime and it doesn't require any special conditions. It just looks like an execution when the guy is low health. Similar to any axe move kill. The R3 execution is supposed to be special and unique.