Thank you, someone makes sense and fucking understands. To add to your 1st point, the reason they burned off is because those things were as real as anything else on an Edo's body, they weren't. When he got revived, nothing could go there because one of his eyes is in one of Tobi's jars, and the other is in his left eye socket.
You don't lose your EMS, what? We saw Madara use his EMS and his Rinnegan when he first got Edo Tensei'd...
There's just no point in using EMS since while the Rinnegan is up you can use all of your EMS techniques...the EMS is still there. He only did that so he can get stronger over time to fuck with their head and discourage them, he's been toying with people since he first got revived.