It was never intended to be perfectly democratic.
It was never "intended" to be elected by the public either. Times changes. I'd support making them more like the House of Lords, with less real power. I don't know how people can honestly look at the Senate and not think it needs a serious overhaul.
A major factor is that the most prominent legislators tend to be Senators. It's an institution tailor-made to have prominent members, in comparison to the much larger House, where it's tougher for one individual to stand out.