There are grandmothers and there are grandmothers. Both Gold Meir and Margaret Thatcher were grandmothers when they led their countries. Whether you liked them or disliked them I don't know how anyone could think they weren't tough enough for the job.
https://en.wikipedia.org/wiki/Golda_Meir
https://en.wikipedia.org/wiki/Margaret_Thatcher
Actually, in my experience there's no one as tough as elderly women. Men often get less aggressive, less domineering as they get older. Some become positively sweet and tender, leading many a parent to look at the interactions between grandfather and grandchildren and wonder, "Where was this person when I was a child myself?"
Women, on the other hand can get "tougher", less compromising.
It's my own pet theory that this reflects hormonal changes, the loss of estrogen in women and the loss of testosterone and other male hormones in men.
Whatever the cause, ask older people if they're aware of it, and I think you'll find that it's not uncommon: not universal, but not uncommon.