My boat also has what you might call “floppy” spreaders, but I don’t regard them as being useless.
Firstly, whilst they are free to rotate forwards and backwards the fact that they are held by a vertical pivot pin means they can’t move vertically.
Secondly, the fact that they are longer than the distance the shrouds would otherwise be from the mast means that when rig tension is applied they MUST deflect the shrouds outwards.
If you prevent them from moving down you are right. I have seen boats with spreaders drooping down to the point where the shrouds were going in a straight line up to the hounds. In that case they are completely useless. Other than that you may be amazed of the effect preventing them from moving forward or backward, even with a wooden mast. You don’t need fancy adjustable spreaders to do that, just set them up correctly, then drill a hole and put a pin in it. (A bolt and nut works too). But you are right in that the most important thing is to stiffen up the mast sideways. And that is done by preventing vertical movement of the spreaders and by making sure they are long enough.