Most modern systems (and computers) are sending digital signals where entire frames need to be constructed and reconstructed in a buffer before they can be displayed. Many HD CRT televisions have terrible latency because they’ll take the analog scan line signal, buffer it into a frame, scale it to the native CRT resolution, then scan it back out to the screen. A high end PVM might allow a straight path, but there is maybe one Toshiba HD CRT that doesn’t introduce several frames of latency (iirc).
That said, from 1999 to 2008 I ran 1600x1200 on 19in CRTs and except for professional LCDs, nothing had resolution, pitch, and color that came close. For 2008 was the inflection point where cost and quality of LCDs exceeded CRTs.