No, they do, exclusively. LTE and beyond don’t even support circuit switched calls anymore.
Bellhead wasn’t intended in a derogatory way, just as a reference to the “Netheads vs. Bellheads” schools of thinking about networks.
I do have great respect for historical phone systems and the clever engineers making them work. In terms of absolute reliability, I think VoIP was indeed a step back (although I think that’s mainly due to modern engineering and QA practices than inherent limitations).
(from https://www.ericsson.com/en/reports-and-papers/white-papers/...)
Circuit switched fallback means falling back to 3G or 2G (or maybe CDMA) for voice calls; if such networks are no longer available in a given area, VoLTE is indeed mandatory if voice calls are to be supported. (Which is often mandated by regulations, so networks sometimes even block non-VoLTE UEs from attaching.)