Input lag is probably the biggest issue, but you can get very low-latency screens nowadays! None of them are actually 0ms, but neither were CRTs unless you're measuring only the top of the screen and not the bottom.
If you're using an emulator, there are quite a few filters that can help to recreate that old feel, none are quite right though.
Personally, I don't think it's that the CRT is better than the filters, I think you're just used to the imperfections of a CRT.
Also, I really do think you need a 4K HDR screen (with good HDR, there's a lot of variance) in order for filters to really emulate the look of a CRT.
Also, in a lot of ways a good CRT does look significantly better than all but OLED displays for games. The down side is they're heavy. I used to have two 22" calibrated flat screen displays that I loved, and only very recently are new displays visual quality on par. I stopped using them more because of space and size than quality. They weighed 85# each and had a permanent bow in the desk I was using back then. Moving 3x in one summer I decided to go with flat pannel. Not as good, but was doing less design work and more programming since then.
It actually can on a really good hdr tv! And there's no reason a crt filter couldn't add static.
Just looking at those pictures I got a faint whiff of wood and warm plastic from 40+ years ago.