As an ex (many,many years ago, even before I had children!) dental nurse it is VITAL to clean teeth from the moment they appear!
Yes, they will fall out, but while they are there and in good condition, they act as "space savers" for the teeth that are to come! Plus it is all part of establishing good practice/habits!
A friend of Mr P's who's child had horribly rotten milk teeth, due to atrocious diet and poor oral hygiene, now faces a long battle to get even a reasonable set of teeth, braces etc are just a small part of it.
SIL's mother sounds as if she is living in the dark ages!
She might even be putting aside money for DGD as we speak, so that she can pay for entire tooth removal & dentures for her 21st birthday!
VERY CROSS OF DEVON