Why are there no tube televisions anymore?

I still have a clear memory of helping my Dad pull 15-20 tubes out of our b&w console TV once or twice a year, when it was acting up, and driving to the Bernstein-Applebee electronics store where we’d kill an hour or so testing each one a couple times. We’d get several that rated "good" a few that rated neither good or bad and 2-3 that tested as "bad". We’d buy new replacements for the "bad ones, put them all back in the TV, cross our fingers and turn it on. Sometimes it worked and sometimes We’d have to go back and buy replacements for the ones that tested inconclusive.
It was a pain in the rear and waste of time.
I don’t miss tubes in TV’s at all.
I also remember that TV repairmen did housecalls then and kept quite busy.
My father and I built a Heathkit mono tube-amp for our 45 player and a guitar amp that I used in a terrible garage band in the 60’s. The Heathkits were rock solid.

There isn't a 4k tv made that has a native refresh rate of 240hz.

Size, weight and cost.
The last large crt tv I worked on was all crt inside. The plastic case was molded around the tube.   I think it was a 32". The circuit board was only about 8" x 10".  And I could lift it myself.  A 32" all tube console took two people to lift.  20 or so tube cluttered inside around the crt. Just to heat the filaments on those 20 tubes took 25amp at 6 volts.  High voltage!  Zenith anode voltage was 35kv on their larger unit.  42.5 rings a bell.  CRT convergence was touchy to get a sharp image.  With age the crt would go gassy.  The red, blue and green color guns would go weak and need balancing.  My dad spent $850 in the 60's for our color tv.  I kept it going into the 80's.  Glory hallelujah they are no more.  

Not a valid comparison.

CRT TVs worked on an entirely different principle to those of today's flat screens.

Apart from transistors and, for those that like it, digital, today's hi-fi uses the same technology as yesterday's, going back nearly 100 years.

You might as well ask why there are no horses and carts.

To gamers refresh rate is not the only factor, although the higher the better. The other factor is latency ... the delay between the moment the video info left the PC and the moment it’s displayed on screen, caused by the built in digital image processing. When watching a movie latency plays no role at all, but to competitive gamers this delay impacts their reaction time in a negative way.

Most modern TV sets have a ’gaming mode’ via which (most of the) image processing is bypassed and latency is minimized. But still there’s a delay of a couple of ms. With a CRT this latency is zero.