Well, I am open for suggestion, as I see things very much from developer view point, which may not be the same as the user experience, well, "may not" ... better say "certainly it is not". Though it would be great to hear other people's opinion as well. Not because I don't trust you seeing this as a problem, just because it was never mentioned by anybody other, and I would prefer to see more opinions.
"It make no sense as its a text window." - what do you mean? it's possible to have mouse in any mode. type in C65 mode "MOUSE ON" and be sure to have the mouse grab mode active, and move the mouse. (the "mouse cursor" is a garbage though since you haven't specified a correct mouse cursor sprite shape, but it's just for to demonstrate that it may be useful in default c65 mode even without any graphics).
Oh yes, the default OSD colour and alpha transparency is just "some" value I put there without any study too much, what value would be useful, indeed.