I can see advantages in what concerns no backstay (uncluttered transom and fuller main sail). I can also see some disadvantages regarding performance sailing in what regards control of the sail shape and probably a lesser resistance to breaking.
regarding a free mast, it has the advantage of simplicity, to put in and out but not to break such a mast has to be flexible and that means that the sails would change shape without any control of the skipper.
That would be a no no in what regards any kind of performance sailing.
To be able to stand alone, a mast would also have to be stronger than a stayed mast and that means more expensive and that matters a lot.
Regarding resistance to breaking, I don't believe that a free mast has the same resistance to breaking as a stayed mast. I mean the same mast with and without stays.
There are others that think otherwise (not many because we don't have a lot of free standing masts on cruising boats). The big defender of free mast is Eric Sponberg .
Here you can read what he thinks about the subject:
State of the Art
Regards
Paulo