First...no, they don't. I mean, they DO operate, but games like shooters either limit the matchmaking by regions or people simply don't play them if they do get the problems of high PING at all. They didn't magically solve the problem at all. They just eliminate the player base which have a problem.
Then there are some hardcore people that actually do play. But on your screen...they will just seem like crappy players.
There are other methods to mitigate the issue based on CLIENT-SIDE calculations, but that makes the games prone to cheating. That's why Square Enix doesn't want to do that, because they don't want to spend money on real quality security to prevent client-sided cheating. Look at the bots. They don't even care about investing in dealing with them, even though some are painfully obvious and a good system would automatically eliminate them within minute from the characters being made (teleporting or standing in player-unaccessible places anyone?!). But alas...even they cannot fully solve the issue.
On a different note, I'd say that being one of the most popular MMO games out there, FFXIV DOES operate fine as is.
It seems you gravely misunderstand something. I don't ask to be catered to. It is Square Enix that decided to cater to me and I'm just taking advantage of that.
That's also the cost of having a "world wide" game. This IS advertised as a global game and it DOES allow people to enter ANY server. So it should be consequential and make it PLAYABLE as chosen. If the servers were region restricted before I bought it...sure. I'd have zero issue with that. Developers choice. I can decide whether to buy the game or not. But it was Square Enix that WANTED people like me to get the game, subscribe and play it (well, not really, they don't want us to play it, it's ideal for them if we pay subscription and never log on...). So they reached out to players like me and made the game that way.
I'll reverse your argument. It's your choice to play this game if it have a combat system that you find unappealing. You can look for a different game, more action-packed. There are tons of them. If you are in NA, your horizons are WAY bigger than mine in all things digital, gaming, entertainment and what not for less money than for me to boot. So don't come here and give subjective arguments to counter objective arguments. I merely stated the reason for high cooldown. That's all.