You are right, Annie, we are lucky to have unstayed masts, with all the advantages and economy entailed. I've been thinking about this quite a lot lately, since the passing of Tom Colvin.
As most of us probably know, Tom always espoused 'lightly stayed' masts for his Chinese rigs, and believed this was the way the Chinese did it. Given that he had experience, as a sailor of a working sailing ship in south China in the first half of the last Century, of sailing working junks, he should know.
It is fairly well-known that junks around Guangdong have used lightly stayed (shrouded?) rigs for at least a couple of centuries, possibly more. Many believe this was an adoption of Western techniques after European ships became regular visitors from the 17th Century onwards. The Chinese did not change the way they did things lightly, but knew enough to recognise and use a good thing when they saw one. It is equally possible that they developed this refinement independently, but given it's absence outside of areas influenced by European ships, probably improbable.
Like Tom, those junks seemed to use fairly lightly stayed masts with little tension in them. Tom believed stays on the Chinese rig should not be used to support the mast, but simply to contain the 'whip effect' in a seaway, particularly with metal masts subject to fatigue failure. Given that both Ilala in the 1966 OSTAR, and Lexia in the 2013 OSTAR lost their masts in very little wind but while rolling around in a sloppy sea after a blow, there appears to be evidence to support this theory.
If people don't like permanent shrouds either side of the mast, it is possible to have the same effect by running the halyard back to the cockpit via a block on the rail, with perhaps the spare halyard running to the opposite rail.
Any opinions?
Edit: For an interesting insight into this issue see section 10.5 of Cutting the Dragon's Tail, by David and Lynda Chidell, who built and sailed one of Tom's designs, and stayed all three masts.