I imagine a lot of the discussion of the elegance etc is all post factum to whatever functional advantages it provided to the various cultures that selected it as their weapon whose survival still very much depended on their talent at war.

Nah, don't ever underestimate the role of fashion in these matters.

Today, you might ask "Why do people spend thousands of dollars on a watch, what functional advantages do these watches provide?" The functional advantage is demonstrating that you have the means to throw a lot of money at a trinket you wear on your wrist. But to convey masculinity, such a trinket should, nevertheless, have some theoretical functionality that conveys a certain degree of readiness for action and adventure. So a diamond-studded bracelet won't quite cut it, but a Rolex Submariner or a Tag Hauer Formula 1 or a Bell and Ross Aviation, or something else with a name connoting action hero stuff, will do the job nicely.

Swords were the men's watches of the 17th and 18th Centuries -- fancy and expensive accessories that hinted at a life of action and adventure, but were rarely used in that capacity. They were essential courtly wear, but not because sword fights were constantly breaking out at court. In fact duelling was quite illegal, and you were involved in an affair of honour, you generally preferred to keep it as far from court as possible, and especially in later years you might resort to pistols even then. No, you wore swords at court because swords were the prerogative and therefore the badge of the aristocracy; they served as a declaration that you were a gentleman, a man of honour, and a man of action. However, just because you wore a sword did not mean you had any real intention of using it, any more more than your average investment banker uses his watch to time his Formula 1 laps or measure his time remaining on a shark hunting dive.

Because the sword would in all likelihood remain in its scabbard, the most important part, for the owner and for collectors (but not, unfortunately for students of fencing) was the exposed hilt. Weapon and hilt styles that could accept a lot of decorative treatment without battering your thigh black and blue were more popular than utilitarian styles that would serve you better on a battlefield. Broadswords were practical soldiers' weapons, but made for inelegant court weapons. Rapiers were oh so fine, although a bit heavy and clumsy to be honest. Some courtiers mounted wooden blades on their rapier hilts to make them a bit easier to manage. Small swords were damn near perfect -- pretty, light, and unlikely to trip other gentlemen in a crowd, or rustle ladies' dresses. Not necessarily that great for fighting, however; once they were no longer worn as fashion items in the 19th Century, they evolved into this, which was far more practical, but rather ugly by comparison.

Samuel Pepys lived at the end of the rapier/start of the small sword era, and makes a few mentions of his swords in his diary. For the most part he only mentions them as fashion accessories, for example:

and in Fleet Street bought me a little sword, with gilt handle, cost 23s., and silk stockings to the colour of my riding cloth suit, cost I 5s., and bought me a belt there too, cost 15s.

or

Up and this day put on my close-kneed coloured suit, which, with new stockings of the colour, with belt, and new gilt-handled sword, is very handsome.

He occasionally rides home with the sword out as a precaution in a bad neighbourhood, and on one occasion he is attacked by a dog, and doesn't even think of using the sword to protect himself. When he makes mention of actual fights, it is usually in a gossipy and disapproving manner, so even by this date (1660s) the sword's functional purpose has become quite secondary.

Now, the symbolism of the sword obviously goes back much earlier than that, back to pre-gunpowder eras in which swords were honest weapons. But a lot of the mystique of the weapon arose in the semi-literate states of the early middle ages, when swords (especially long swords of the mounted/knightly classes) were expensive pattern-welded weapons, compared to alternatives like axes and spears. But once again, that suggests that part of their mystique was their price, and what that said about the owner.