In my experience, I've almost never seen お金 without お. I'd guess the reason is that money is just intended to be treated with respect, regardless of who possesses it. There are lots of other words that kind of absorbed the お, like お母さん or お茶.
Absorbed the お? I'm pretty sure we still use that quite often in the examples you gave, although, like you said, it's a more respectful or polite way to say those words. Also ご~「御」, both are written with the same kanji and considered a type of けいご (敬語).