Enough can't be said about singing ON the mic.
I coach performers about this as well, over and over.
Quite often, they will ignore my repeated requests.
Like ST, I just have to let it play out with them barely being heard.
One reason is probably their conditioning to singing with traditional PA, "let the sound man turn me up out front" syndrome.
The other, and I was guilty of this as well, is fear of hearing yourself like you really sound.
It can be a shocker, and I struggled, wanted to back off when I feared I wouldn't hit the notes, I could tell I was slightly off-key.
My friend Nathan, told me to "Sing Out, and Make Grand, Sweeping Mistakes!".
This approach lead me right to the woodshed to practice, and learn to belt it out, best I can.
I am still a soft singer, but I stay on the mic, and give it all I've got.
Which isn't a lot, but with the L1 behind me, I'm confident it's being heard.