Why on earth would you think each player having their own subjective square names is a good thing? It's one of the main reasons Descriptive fell out of use.
You should at least address some of the points he made. Assume you are a novice who is just learning the game, and you read somwhere that you should put your rooks on the 7th rank. But you're Black so you end up putting them on the wrong rank. The problem is that traditional terms developed when Descriptive notation was the vogue in the US and UK was not adapted when the West converted to Algebraic.
When I learned first learned chess with Descriptive, I noticed that when there was some ambiguity, they would specify QNxP or KNxP if either Knight could make the capture. Same with the Bishops. But when I first tried to record my own games I was very puzzled as to how you could keep track of which Knight was the Queen's Knight and which was the King's Knight, once the game was in the later stages and everything got scrambled. So, I always set up the starting position with the Knights facing inward, and the Bishop's, as well (with the "smile" facing the center.) And since the rooks are perfectly symmetrical, I actually put a little pencil mark on the bases of each!
Sounds stupid? Of course, but I was 9 years old and very conscientious.
Funny thing is, more than 50 years later, I still set up my pieces with the Knights and Bishops facing inwards. Although I no longer put pencil marks on my rooks.
Interesting point you bring up, but it supports algebraic notation. With descriptive notation, each square actually has two descriptions (one from each side) and each description can describe two squares unless the colour is specified. Ranks also need colour to describe the location, e.g. White's 7th is Black's 2nd. The drawback for algebraic is that everything is from White's perspective and thinking about Black requires an upside down and backward perspective.