The tubes start generating X-rays above 5kV or whatever(some docs say 15kV), and you need leaded(literally Pb melted in) glass for the screen to block it, unless you could find a substitute material(Sn nanoparticles or something) or you're fine with <5kV brightness for the tube whatever that amounts to. So you can't pitch it as a nicely eco friendly product, and the glass can't be easily recycled(Pb removed from glass).

Otherwise they're not THAT complicated. They're a lot like lightbulbs. Certainly not as exotic as LCDs.