"Committing suicide" used to be a crime in many jurisdictions, and "commit" often has crime connotations, so "dying by suicide" is considered a kinder and more accurate term these days. (I still say the former sometimes, though, as that's what I'm used to.)

I do somewhat agree with you, as it feels off, but I don't think it's in the same category as "unalive". "Dying by suicide" is as clinical and non-euphemistic as you can get, really. "Killed himself/herself/themselves" is a bit more direct, I suppose.