The form of phi – Φ – from the Greek alphabet is an historical antecedent for these English alternates. I don’t think it has much to do with the letter O, though.

Plus, it helps to structure the inner whitespace. This way, you can have a larger (wider) O that doesn’t look out of place when standing next to darker, denser letters like M.
A dot would serve the same purpose, see for example Barnbrook’s Mason, or Tiemann’s Orpheus (revived and extended by Canada Type). CastleType’s Goudy Trajan offers an alternate O with a cross in the counter.

It might also be worth looking at the ‘O’s in blackletter typefaces, e.g. Alte Schwabacher, Fleischmann Gotisch, Goudy Text, Royal Bavarian.