>Before HD, almost all video was non-square pixels

Correct. This came from the ITU-R BT.601 standard, one of the first digital video standards authors of which chose to define digital video as a sampled analog signal. Analog video never had a concept of pixels and operated on lines instead. The rate at which you could sample it could be arbitrary, and affected only the horizontal resolution. The rate chosen by BT.601 was 13.5 MHz, which resulted in a 10/11 pixel aspect ratio for 4:3 NTSC video and 59/54 for 4:3 PAL.

>SD channels on cable TV systems are 528x480

I'm not actually sure about America, but here in Europe most digital cable and satellite SDTV is delivered as 720x576i 4:2:0 MPEG-2 Part 2. There are some outliers that use 544x576i, however.