I believe the thick front (leaded) glass is to try to block the produced x-rays.
People were starting to get scared of the cancer those xrays might produce, and I suspect CRT manufacturers predicted a huge court settlement for cancers caused by TV's with insufficient shielding.
So far, it seems that hasn't materialized - not, I suspect because those xrays didn't cause cancer, but because it is simply impossible to produce any kind of evidence of cause/effect.
Only the oldest CRTs used leaded glass for the front, because leaded glass gradually turns brown on exposure to X-rays. More modern CRTs used glass with barium and strontium for X-ray shielding in the front. They still used leaded glass for the back and sides, presumably as a cost saving. I don't see any reason why you couldn't use the barium-strontium glass for the whole thing. Alternatively, CRTs could be made with ceramic bodies like Tektronix used to do.
The energy of the X-rays produced is limited by the CRT's acceleration voltage. The electrons get almost all of their energy from the field produced by the acceleration voltage. Electrons can produce photons when they hit matter, and one electron produces at most one photon, so by conservation of energy the X-ray cannot have greater energy. Smaller CRTs typically use low acceleration voltages, which means the X-rays are low energy and thus easy to block.
AFAIK, the shielding was also just very effective. "Soft" x-rays (below 50-100 kV or so) are rather easy to shield and what screens had was pretty overkill.
People were starting to get scared of the cancer those xrays might produce, and I suspect CRT manufacturers predicted a huge court settlement for cancers caused by TV's with insufficient shielding.
So far, it seems that hasn't materialized - not, I suspect because those xrays didn't cause cancer, but because it is simply impossible to produce any kind of evidence of cause/effect.