If you're singing operatic arias and such, you have a whole orchestra (and perhaps chorus) to contend with, so you pretty well have to sing them in the keys they're written in. But . . . if you're singing, especially, folk songs, you can sing them in any key you want, presumable one that suits your voice.
I''m not just making this up. I studied music formally at the University of Washington School of Music and the Cornish School of the Arts, and the word is that unless a song is written for a specific voice (i.e. tenor aria, or the bass part in the last movement of Beethoven's Ninth Symphony, you can sing it in any key you want. There's a difference between a song (any key) and a "vocal part" (specific, fixed key).
I've never been able to understand pop or jazz singers who say things like "my key is Eb." That's silly. Unless they have an extremely wide range, I bet I could come up with a batch of songs they couldn't sing in Eb.
One of the problems with singing everything in the same key is that, after a while, everything you sing starts to sound the same.