No, an astute grandmotherly woman doesn’t embrace children who don’t know her without significant cause.
Such “embracing” is what Joe Biden does.
My grandmother did. And most loving elderly women I know do so.
I would hate to meet the old woman who pissed you off so much that you think it normal for them to be evil and cold towards little children.
When I was a child, I remember many an old lady who would embrace me and show me grandmotherly attention.
Elderly men on the other hand usually showed me the type of respect a boy needs from older men to know what we should be like when we get older.