I've seen TVs where the entire AC cord had glowed red, and melted off all the insulation 'til the wires touched and blew the house breaker. RCA color tube sets were famous for broken circuit breakers, and uncaring technicians would slap a who-knows-how-heavy pigtail fuse across the breaker.
As far as house fires caused by TVs, yes plenty
. However, most that happened in my time were by early Zenith and Sylvania solid state sets of the 70s with ECG-500-ish triplers. When those fail, they throw out a flame like a blowtorch, so heaven help you if the TV is a plastic or wood cabinet. When those flame-ups happened, it didn't seem to draw too much current to trip a breaker or blow a fuse. The other big fire-starters were CTC-15 & 16s with bad on-off switches. They would fail when the TV was OFF, in the middle of the night or when the owner might not be home. There may even have been a recall on those, and I replaced plenty of switches that had burst into flames, usually just burning wires. However, I personally saw two of them which had flared up, burning all of the wiring on the tuner chassis, and catching the plastic channel wheel which in turn burnt a hole in the top of the cabinet.
Charles