Bono's voice issue is something I've been thinking about a lot. I'm a doctor, so I'd say I'm also a bit knowledgeable on the medical side of the question.
My personal thought is that the change that we all notice between every U2 record should be blamed on a lot of reasons, concurrently. I think it's a mix of aging, smoking, surgery (not sure if this really happened, but there are people on the forum suggesting so), change of singing style, singing lessons. I'd suggest that the first two, smoking and aging, are the most likely. Sure enough, smoking has helped Bono's voice to develop a lot between War and Rattle&Hum; (developing also that lower register you're referring to) his voice became stronger and more "scratchy", but aging has played a strong role too. Things started to change after Rattle&Hum, particularly after the Lovetown tour. Bono struggled a lot during that tour, and his voice weakened a lot during those months, for a bunch of different reasons. First of all it's known that he over-used his voice, screaming his lungs out every night. Let me say that stressing your vocal folds more than you need to will weaken a lot your voice in causing irreparable damages. Secondly, Bono suffered of some kind of infection that hit his throat. Bono himself said that he had "some pretty psychedelic germs in Australia and that they were having their Annual General Meeting in his throat". In fact we notice that Achtung Baby sees a radical change in Bono's singing. His voice, although still wonderful and kinda strong, is clearly weaker and different. And things have gone worsening in the following years, faster and faster. So it's easy to say that the Lovetown tour is the pivot point in Bono's voice change, if we wanna consider 1988/1989 his peak, talking about his lower register too. In fact I think that he's never hit lower notes than in the Lovetown years.
Talking about today, we gotta say that his voice is totally different, but on the other side it's amazing in a whole different way. Sometimes it's really hard for me to relate today's Bono with JT/R&H/AB Bono, because they really seem to have two totally different voices. My point is that he's not lost his low register, and I'll give you an example. As I said before, it's not low as it was in 1989, but it's clear that he still handles it.
Enjoy
Bono (U2) recites a poem to Anton Corbijn - YouTube