What YogoJen said!
Also, have you noticed that no one would think it's an insult to suggest to a trumpet player that private lessons will improve their skill... but if you say that to an aspiring singer, its somehow a huge insult to them? As if professionals at the highest levels don't have multiple coaches?
My favorite voice teacher said the same thing Jen is saying. She could teach just about anyone to sing better, and for most of us it's markedly better. But yes there will be people who find their limit before others, and some who have found their true instrument in the voice.
What I wish I could do is to "sing casual" with more chest voice. I was brought up with Italian and some English rep. I'm a dime-a-dozen soprano, and so my voice doesn't know what to do with the low notes. Seriously there are some areas where I become like a teenage boy with a warbling voice and I just can't control it. I'd like to think it can be solved as a voice placement issue, maybe the strength of the air pushing the note out.. what I don't want to be true is that my voice has gotten older and is simply set in its ways now. And yes, the problem gets worse as the day progresses and the vocal chords get tighter.
Aperson, have you tried finding a chorus to join, maybe at a school, or a church, or wherever? How I started out was to join Chorus I my senior year of HS, just because I had the free time. The director approached me about taking lessons, and that was when I discovered the joy of the instrument that you always have with you. Sure there's always someone who started really early (too early?), but it's never too late.