There's really only one song which Brad shows up in with main vocals, being UNTIL IT BREAKS from LT. Why doesn't he sing more often? He has a good singing voice. Am I missing any songs or demos where he does sing?
I don't know and would love some objective info here. My own speculation is that Brad very rarely makes his own demos with vocals, and Until It Breaks was one of the few times where he composed and sung that part himself, and the band decided to stick with his vocals coz they fit the spacey ambient soundscape and stood out from everything else. Similar to how Mike's vocals on No Roads Left were originally just supposed to be a blueprint to instruct Chester, but when Chester sung it, they decided Mike's vocals sounded better on that song
While it was a neat surprise on Until It Breaks, I don't think his voice necessarily fits the rest of the band's sound. I can't imagine many instances where his performance would be better than Chester, Mike, or now Emily.
I'd like to hear him sing more (variety is always fun), but I very much doubt it will ever happen. I just don't think he has any desire whatsoever to sing lead. That being said, based on Three Band Terror, I do think his voice would work quite nicely on something folky or acoustic (where you can maybe get away with being a less technical singer, I suppose). Speaking of which, this is a big area that Linkin Park have flirted with (The Messenger, Final Masquerade acoustic version, some influences on Living Things, various live performances), but have never explored fully in its own right. If the band are still interested in every album sounding like nothing that came before (as they were in the Chester era), then I would be surprised if we don't get a more folky/acoustic project coming out eventually. In my head I'm imagining something like the softness of One More Light mixed with the rawer production of The Messenger/The Hunting Party/etc. If Brad were interested in singing on something like that, it could be quite interesting as a change.