You can have a Hi Def CRT. In fact there are many different types of high DEF TV's
LCD, Plasma, CRT, LCOS, DLP, RP, LCDRP...The list can go and is.
A CRT isn't tubes it is 1 big tube that shoots lots of electrons to the screen. If you shoot enough small electrons in a given area you can create a HD CRT.
What makes it high def is lines of resolution it can support at either progressive or interlaced. hence 720p or 1080i or 1080p.
Why Computers don't look good on older CRT TV's has to do with a variety of factors, Refresh rates (how fast the screen can clear the image) and interlacing (the bad flickering effect) being 2. Other things is resolution, picture quality as yit get further from center (I can't recall what this is called, but it's why flat screens/panels are better monitors)
Hope this helps some