I had a 12" b&w portable TV, bought new in 1975, that worked well for three years, then one day I turned it on and saw a curl of smoke coming up through the ventilation slots in the cabinet. (No raster, of course.
) I had no clue at the time as to what was burning, but seeing your post reminded me that it could have been the yoke, one winding shorting to the other, and possibly a resistor (as Bill Cahill suggested). Typical for a small, cheaply made, tube-powered offshore-brand portable.
Talk about BPC! To the best of my knowledge and belief, no one used that term in the 1970s, but it certainly would have applied to a lot of the small, cheap no-name offshore-made tube-type portables available at the time. The sets may have worked halfway decently when they were new, but they would develop problems after a very short time, after which many of them were junked. Today's no-name flat screens are like that too.
I guess this just goes to show that there were cheap TVs on the market as recently as the 1970s, and quite possibly even earlier than that. I don't know exactly when these junky sets first appeared on the market, but my best guess is the late 1960s. I had a Sharp 12" portable in 1970 that worked well all of three years (!), then developed a tuner problem which I was able to work around, at first, by propping up the VHF tuner shaft with a screwdriver; however, the set developed more serious problems a year or so later, after which I junked it. Too bad, because that set had a great picture, even on a monopole VHF antenna in the near-fringe TV area in which I lived at the time. Further, since it was made by Sharp (this was years and decades before offshore companies started slapping well-known TV manufacturers' names on BPC sets), I expected it would last longer than it did.