While I agree there needs to be something to help a players performance, I don't think this is the right solution.
For starters, While it might do a good job of accurately depicting DPS numbers on a stationary target, it will do nothing to help in the fight itself. With added mechanics to deal with, it just is not the same. Even if you add AoEs or other mechanics to do, it's a different scenario in the fight itself where you have to coordinate the mechanics with 7 other people.
A healing Dummy is also an odd one to do as a healers DPS output is related to the other people in the party, the more unnecessary damage they take, the more the healer has to heal. Having a dummy you have to heal every now and then that takes consistent damage is not going to help in the real fight situation.
As for a tanking dummy, between tank busters, hard hitting adds, raid wides etc. there are many ways a tank can mitigate damage, but you cannot effectively account for all of them in a dummy fight, meaning, it, again, is not an accurate comparison between dummy fights and an actual encounter.
Then I'll just add the most glaring and obvious thing. Just because someone clears the dummy, doesn't mean they will consistently be putting in that much effort all the time.
To take a slight tangent, I want to talk about how effectively you can tell someone is doing a good job or not. For tanks and healers, it is easy. Is the tank positioning right, are they mitigating effectively, etc. For healers, are they keeping the party alive, are they mitigating/regening when needed, are they throwing out damage spells when they can etc. All these things can easily be seen my anyone in the fight, you know when something goes wrong when the tank dies to a tank buster, when the healer doesn't apply proper healing etc. It is there for everyone to see and it's generally easy for someone to point out that one tank/healer who isn't pulling their weight and call them out for it. Now, a DPSs only job is to do as much damage as possible. If you fail an enrage due to DPS, how do you know who the weak link is? In theory you don't know how anyone performed, was it 1 DPS, 2 DPS? Ok, if someone dies, you could point the finger that way, but I've seen cases where the DPS that died still managed to do more than they DPS who was alive for the whole fight. In short, there is no way at all for the group to find that weak DPS player and go, you need to improve. You can do it with tanks and healers, but for some reason, you cannot do it for DPS. Why should it be one way for tank/healer and another way for DPS.
With that, slightly long tangent out of the way, back to the issue. the main issue is that fact we have fights that have an enrage based on how much damage your party puts out over a certain time limit. This gives you a minimum DPS limit your group needs to hit if you are to succeed in the fight, no ifs or buts. However, the game gives no feedback in the fight as to where the improvement needs to be made. Yes, DPS needs to improve, but who? Which person is not pulling their weight. Again, tanks/healers are under scrutiny if something goes wrong, and the problem person can easily be dealt with, whether its telling them they need to improve or kicking them and getting someone else, improve your odds of beating the fight. However, since you cannot do that with DPS....you are at a standstill. You don't have the DPS to beat the fight, you don't know who is causing the DPS issues, so you either keep at it until either the timer runs out, or you get a miraculous victory, the alternative is making a new party from scratch and hope for the best. DPS players are essentially getting a free pass to be an underperformer, but they might not necessarily know that they are, and that's the thing. People don't have to tools to tell someone, you need to go and learn a proper rotation before you think about coming back in again.
It all comes down to the lack of some sort of DPS meter as a tool that should be used to gauge party performance, in the same way you can gauge a tank or healer and no, having something at the end of an encounter after you have cleared it isn't good enough. If you are already struggling with DPS somewhere, having a performance rating at the end isn't going to help here and now. Having a dummy act as a gate isn't going to help here and now. However, since SE don't want to add a parser, we will forever be stuck in a state where we have encounters with a minimal DPS requirement, but no way of knowing where that weak link is.