It's a server/netcode problem. Because the server has to tell every player what every other player in an area is doing, as you add players you create a non linear growth curve in server load. Ie: One group of 100 in one spot is more server load than two groups of 50 at opposite sides of the map, despite having the same number of players. Severely so, in fact. Every MMO has this problem at some level of concurrency (it's just an inherent reality of how concurrency works), but XIV's limit is low enough that we hit it a lot more often.
On top of that, the servers don't prioritize traffic. It'll lose track of half my party but is still sending combat log data on 90 other people who I don't need that data for at all. This could be significantly improved both by making Eureka instances have fewer people (the faster fix) and by reducing the traffic load between server and client, thus pushing the limit higher before gameplay is affected (the much harder but better fix).