While analog video did not have the concept of pixels, it specified the line frequency, the number of visible lines (576 in Europe, composed of 574 full lines and 2 half lines, so some people count them as 575 lines, but the 2 half lines are located in 2 different lines of the image, not on the same line, thus there are 576 distinct lines on the height of the image), the duration of the visible part of a line and the image aspect as being 3:4.
From these 4 values one can compute the video sampling frequency that corresponds to square pixels. For the European TV standard, an image with square pixels would have been of 576 x 768 pixels, obtained at a video sampling frequency close to 15 MHz.
However, in order to allow more TV channels in the available bands, the maximum video frequency was reduced to a lower frequency than required for square pixels (which would have been close to 7.5 MHz in Europe) and then to an even lower maximum video frequency after the transition to PAL/SECAM, i.e. to lower than 5.5 MHz, typically about 5 MHz. (Before the transition to color, Eastern Europe had used sharper black&white signals, with a lower than 6.5 MHz maximum video frequency, typically around 6 MHz. The 5.5/6.5 MHz limits are caused by the location of the audio signal. France had used an even higher-definition B&W system, but that had completely different parameters than the subsequent SECAM, being an 819-line system, while the East-European system differed only in the higher video bandwidth.)
So sampling to a frequency high enough for square pixels would have been pointless as the TV signal had been already reduced to a lower resolution by the earlier analog processing. Thus the 13.5 MHz sampling frequency chosen for digital TV, corresponding to pixels wider than their height, was still high enough to preserve the information contained in the sampled signal.
No, the reason why 13.5 MHz was chosen is because it was desirable to have the same sampling rate for both PAL and NTSC, and 13.5 happens to be an integer multiple of both line frequecuencies. You can read the full history in this article:
That is only one condition among the conditions that had to be satisfied by the sampling rate, and there are an infinity of multiples which satisfy this condition, so this condition is insufficient to determine the choice of the sampling frequency.
Another condition that had to be satisfied by the sampling frequency was to be high enough in comparison with the maximum bandwidth of the video signal, but not much higher than necessary.
Among the common multiples of the line frequencies, 13.5 MHz was chosen because it also satisfied the second condition, which is the condition that I have discussed, i.e. that it was possible to choose 13.5 MHz only because the analog video bandwidth had been standardized to values smaller than needed for square pixels, otherwise for the sampling frequency a common multiple of the line frequencies that is greater than 15 MHz would have been required (which is 20.25 MHz).
From these 4 values one can compute the video sampling frequency that corresponds to square pixels. For the European TV standard, an image with square pixels would have been of 576 x 768 pixels, obtained at a video sampling frequency close to 15 MHz.
However, in order to allow more TV channels in the available bands, the maximum video frequency was reduced to a lower frequency than required for square pixels (which would have been close to 7.5 MHz in Europe) and then to an even lower maximum video frequency after the transition to PAL/SECAM, i.e. to lower than 5.5 MHz, typically about 5 MHz. (Before the transition to color, Eastern Europe had used sharper black&white signals, with a lower than 6.5 MHz maximum video frequency, typically around 6 MHz. The 5.5/6.5 MHz limits are caused by the location of the audio signal. France had used an even higher-definition B&W system, but that had completely different parameters than the subsequent SECAM, being an 819-line system, while the East-European system differed only in the higher video bandwidth.)
So sampling to a frequency high enough for square pixels would have been pointless as the TV signal had been already reduced to a lower resolution by the earlier analog processing. Thus the 13.5 MHz sampling frequency chosen for digital TV, corresponding to pixels wider than their height, was still high enough to preserve the information contained in the sampled signal.