Is having a unique word that much of an improvement over "paternal grandmother" vs "maternal grandmother"?
Or is it that you're referring to other relations than those two having unique words? If so then that would seem to introduce its own problems in ballooning the vocabulary.
Maybe English is just happier with the ambiguity?
One word helps make it easier.
I got very tired, very quickly, even as a kid, of saying "Grandma on my Dad's side".
I had two Uncles with the same name, again, "Uncle <foo> on my Dad's side" is a PITA after awhile.
This is because English sucks at tree relationships. Other languages are much better at this.
For example, Mandarine Chinese has unique words for each side of the family tree (e.g. unique word for Grandma on mother's side vs Grandma on Father's Side), and also a rather logical system to describe how you navigate the tree.
Chinese isn't even unique in this, it is just that English is really really bad.