On Music: Does Key Signature Matter

A good start maybe from here which I came across in my online search. The other parts of music theory is obvious of their quality, but whether if it matters which key a music is composed in, often becomes a bit vague for me. I've heard various experts make a big deal out of it, but then you have to be a good sight-transpose musician if you are ever to be considered professional in your play. As if all music can just be transposed away without concern.