Looking at in a different way.
Rub your left hand up and down on your stomach, at the same time with your right hand tap your head. Keep doing it.
Now while you are doing those two things …….Sing. My guess is you can’t sing much better doing that, than you can while playing.
Just like with the guitar you are trying to do 3 different things at the same time. A lot of time has to be invested to get past that. Sounds like you will invest it.