I hate the word too. I remember it being used when I was a child and someone commented on a hair-ribbon I had on. I thought then, and I still think now, that it means 'showy', 'put on', 'done for show'. Linda Snell's voice, to me, is posh, because it's studied and not her real voice. I don't like it when people who speak with what used to be called 'received pronunciation' are labelled 'posh', because in most cases that voice is real to them, it's what their parents spoke and their parents before them. It's not consciously produced or done for effect.
I worked in three boarding-schools and also went to two. There was a healthy mixture in all of them. People who could afford to send their children away to school and arrived in huge shiny cars and people who scrimped and saved to send their children to boarding-school because they valued the available opportunities, and arrived in old and usually muddy cars; which of those were the posh ones? Of course those are extremes. All sorts of children were there, some blissfully happy, others not so happy perhaps because their parents were engaged in bitter divorces - it is impossible to generalise. I was aware of a lot of kindness among the children - as well as some spitefulness. Society concentrated in an institution, I suppose. They had to learn how to get on with all sorts.