This is one reason why I'm lead singer in my band (as well as bassist, and other instruments if required).
I'll talk about myself here since it's my main reference in this situation, sorry for the self centered post. I'm not a great singer in my actual voice-box, but I have pulled off being a very good lead singer in the right environment, song/recording, style, etc.
As opposed to many pure-singers who work mostly in popular music, I'm a musician with a lot of theory knowledge and experience harmonizing and improvising in various genres.
Keys/harmonies/melodies are easy for me to keep track of and come up with fast...
...while a singer with a truly great voice, due to their physiological make-up, but without the ear/talent/training/knowledge/experience I have, will sometimes have trouble coming up with the right notes or fixes or harmonies quickly, if at all. From what I've experienced over the years.as it does help immensely to improve one's self awareness.
Am I as good a singer as a great dedicated front man? No. Am I as entertaining to watch or as magnetic of a personality on stage? Nope.
When you hear a problem with your singing, you try to fix it. training/experience/theory/musicianship helps me here, but pure only-singers can have all that too, and some are brilliant at it.
I had the privilege to watch Jon Anderson from Yes compose complex vocal lines in real time with YES, and he was thinking silently to himself while the others sat silently waiting for his instructions in this arrangement, and then he started giving them instructions in full on chords, complex ones with jazz voicing etc, all from inside his head, composing in his mind like Mozart in the movie Amadeus.
That's sort of what I do (and lots of experienced musicians do) in my mind when I compose or arrange (for voice or instruments), but many singers can't seem to do that. Therefore, it's more of a challenge for them to know what to create based on music around them, or how to fix it when they don't fit it, or sometimes even when to realize there is something that needs fixing.