I'm a pretty bad vocalist too!
I'll likely never be much better than I am now. I've been singing my whole life, I've taken lessons, I've performed in choirs. It's not that I can't hear when I'm off pitch so much as it is that I've never been able to develop the vocal control to fix it.
There are about 4 notes I can hit consistently. When I'm singing often, or at least when I have sung often in the past, I was able to stretch that a little bit. I can improve, I'll just never be what we as a society have come to recognize as Good.