Yes, way back when the TV industry was being invented they needed every trick they could conjure up. So, using the power line as a field synchronizing rate did solve some problems. How much so, I am not sure. That went away fairly quickly. But the numbers remained.
Back in those ancient days, the TV cameras also did not have any definite relationship between the horizontal and vertical sync rates. I mean, just how do you design a TUBE circuit that multiplies 60 Hz up to 15750 Hz, with stability? I do not want that job. So yes, if you are taking the vertical scan rate from the power line, then the horizontal rate will be drifting free of that vertical rate. This went away real fast as TV developed. And the two frequencies were tied together in a strict relationship, both in terms of frequency and phase.
Among other things that needed this relationship was the serrated vertical sync pulse in the vertical interval. Tube circuits in TV sets were ANALOG oscillators that had to be kept synchronized with the sync pulses in the video signal. Remember that the NTSC video signal is interlaced: 262.5 lines forming field one followed by another 262.5 lines forming field two. And those two fields had to be timed to start properly to keep the adjacent lines separated. A small timing error in the start of the vertical sweep could mean that the lines of field 2 could be on top of field 1. So the vertical oscillator in the TV set had to start very precisely (for tube circuits) for both fields. And at the same time that the vertical sync pulse was being transmitted, the horizontal sync information (pulses) needed to continue so that the horizontal circuits did not lose step. So the vertical sync pulses, which were three horizontal lines long, were serrated by the horizontal sync pulses. BUT, if the vertical sync pulses at the start of the two fields were just serrated at the horizontal rate, then one would end with a pulse that is a full H line long while the other would have a final pulse that is only 1/2 as long. That would mean that the OLD FASHIONED tube oscillator circuits would have a hard time starting in the correct time intervals. One would be sooner and the other later. And the lines of the two fields would start to overlap while a black band appeared between them. Not good.
So they increased the horizontal pulses to twice the 15750 Hz rate during the vertical interval for a full 21 horizontal lines. The horizontal oscillator could ignore the extra pulses while the vertical oscillator saw six vertical pulses that each lasted for 1/2 the horizontal line's duration. Both of these serrated vertical sync pulses, with six divisions, lasted for three horizontal lines' time and both appeared the same to the vertical oscillators which needed that advantage in the early days of tube type TV sets.
This is one big reason why the idea of locking the H and V sync rates together was a MUST. It is a major reason why the idea of using the power line frequency as a reference was VERY QUICKLY abandoned. Once NTSC was standardized for B&W TV, there was no more power line reference. PERIOD.
But, as I said, the numbers remained. Part of the reason why that happened is likely explained by the various OEMs of the broadcast equipment and the home TV receivers reluctance to give up any of the market share they had in those industries. There had to be agreement on what was done so that the equipment would be compatible. This need for compatibility was repeated when color TV came along. I can remember the ads for the various TV sets claiming how they were "compatible" with each other and with B&W TV. It wasn't all strickly technical reasons. Some of it was marketing.