I've been thinking of a way to tell to DPS how well or bad they're doing.
There's actually very obvious ways to tell if a Tank or a Healer is underperforming, but that doesn't really apply with DPS outside of DPS checks.

The "personal DPS meter" isn't going to achieve anything. Not only it won't make people want to improve (ie. you can still get away with being bad, so what's the point?) but also the number itself doesn't mean anything outside of any context.

A "party-wide DPS meter" will probably lead to flaming and shaming more than a motivation to self improvement. If a DPS is the last one on the DPS meter, he won't suddenly think "hey, I'm bad! Let show them, I'll improve myself!" and raise his DPS like crazy.
Besides, that will add some pressure on low-skilled player who'll more likely try to focus on doing damage and thus, not properly deal with the mechanics of the fight (ie. get hit by AoE, die a lot more, etc.).

So, what's left? Well, remember this?

It's the "Stylish rank" system in Devil may cry. This system is based on the "style" you have during a fight. There's just an obscure number attached to it "Stylish points", bu you can easily scrap it and just keep the green bar.

This system has a big advantage: you never want your score to go down and want to increase it to see the nice SSS on your screen.

Of course, "style" can't be applied to FFXIV combat style since it has very different variables. But I can very well see an adapted system for DPS class which would take the damage they take and they deal in consideration.
You can even show this "score" at the end of a trial/dungeon to show how everyone was performing. Just like we already have with PvP content.

This kind of "hidden number" system allows new player to understand what's going on immediatly and have a goal to keep improving themselves.
I believe that raising the skill level of each individual like with this kind of things is the key before really speaking about DPS meters, which should be kept for progression content.

For progression content, an ingame DPS meter could be of use, but is not really a priority considering the tools we already have.