In the old TVs, the PLL consisted of a monostable multivibrator set to run sightly lower than the expected line frequency. A signal edge assumed to be the H-sync pulse would retrigger the multivibrator a bit earlier before reaching the end of period. The voltage range was quite limited and so was the frequency locking so I do not see how that would burn the TV due to false sync pulses. The PAL, SECAM and NTSC line frequencies are quite close together, so you could get good H-sync, while the 50/60 Hz difference was often too much for V-sync.
Anyway, the H-sync pulse has an other important duty in OTA reception, since it is also used for generating the a.g.c. signal for the front end RF and IF stages at least in countries, with negative video modulation. The amplitude of the synch pulse is sampled and that value is then used for the _whole_ horizontal line. You can't use the average amplitude of the whole line as a.g.c., since the IF gain and hence average picture brightness would vary depending on picture content.
I have no idea, how they handled the a.g.c. in systems with positive video, such as the 405 line system in UK or 819 line system in France.
That was about 1980, such as the Salora/Nokia IPSALO