FFXIV uses old architecture, plain and simple.

For FFXIV, each server is a physical machine running one copy of the game's server software. You login to a server, and all of your interactions occur on that server. There may be some sharding for instances/duty finder, but if so there's apparently finite resources allocated to those.

GW2 and ESO do not have these problems because of their modern architecture. Every map is an instance, and when one instance is full, they spin up another one. They can probably run 20-30 such instances on one host, and can dynamically provision new hosts automatically when demand is high.

That's how pretty much all modern online services are built whether they're games, social media networks, live streaming services, etc. In FFXIV's case, SE didn't build it that way and it's probably not worth the cost of overhauling the backend to handle a few days every 2 years of heavy load.