A bit of some lost history on dps meters coming from someone who played WoW at release. So back in the day of Everyquest and WoW, there were no damage checks on bosses and you could have a massive crowd of people all pounding on a world boss to get the thing down, with the only real responsibility being the tank had to make sure he kept the thing facing the right way, off tanks were on the ready incase the main tank died, and healers were setup like a conveyor belt to keep the tank and replacement tanks up while the rest of the people just beat on the big loot pinyata.

But there was a flaw in this: The dps could be lazy bums. You might have someone literally fall asleep on their desk and when he wakes up, the fight was over. Heck, I still remember when a buddy of mine went to grab a burger while we were in Molten Core and came back 10 minutes later with the raid lead none the wiser. To the developers this was a flaw, so they added an enrage timer to bosses in order to encourage dps players to actually engage in the gameplay. This happened I think after The Burning Crusade. The thing was, the lack of dps meters made end game content accessible to everything at the cost of quality. No one really cared about DPS unless they were trying to set a record on a clear, so you'd get a lot of Damage dealers mostly picking being a damage dealer for the lower level of responsibility and engagement.

When DPS meters got introduced, it changed just about everything and pushed tons of people out of end game raiding. There were no duty finder easy mode raids: you had normal raids and sometimes an extremely hard version. People would team up and run these end game raids like a business or second job and this lasted for a pretty darn long time. It wasn't until Mists of Pandaria that Raid Finder got introduced, and RF is what set the death knell for the whole "mid-core business like raiding guild". The issue was, damage was still something you wanted to be able to output because they still had enrage timers in content above RF, and at this point everyone was about efficiency, so even non-raiding groups would run dps meters to try and be more efficient.

Now, as far as FFXIV goes, I don't know exactly what prompted them to ban DPS meters in the first place, but I feel that they generally were taking the toxicity of WoW at the time as an indicator that DPS meters are a bad thing for the community. Technically, DPS meters are not a very good barometer of skill. The issue is that a dps meter only cares about numbers and rotation buttons hit: It doesn't take into account something like your ping, or the woes of technology, or if the boss mechanic happens to prevent you from doing damage. It takes a lot of knowledge just to USE a dps meter properly and honestly, I feel the issues with the dps meter go outside of the DPS meter and into game design itself.