[RobT]

“Personally, I’ve always questioned the true historical and cultural value of the objects we collect, particularly when it comes to antique arms. Is their worth found in craftsmanship, aesthetic beauty, or perhaps the legendary aura we project onto them? Are these objects truly part of our cultural heritage — or only a select few? Or are they simply "big boys’ toys”?”

I don’t think it is possible for anyone to point to any other object in the world that holds a cross cultural position equal to that of the sword. For example, religious texts are only highly regarded within the confines of their particular religion. Outside of that religion they may be regarded variously as irrelevant, nonsensical, incorrect, or even blasphemous.
The importance of the sword goes beyond “legendary aura”. The sword is the soul of the samurai, the defender (and promulgator) of the faith, the sword of justice, the fateful lightning of the lord, etc.
Until fairly recently, the sword (or its smaller iteration, the knife/dagger), was part of entitled male attire around the world. In many instances, just by looking at the weapon worn, a viewer could deduce the wearer’s group affiliation and the sumptuousness of the weapon accurately displayed the wearer’s wealth and position in society.
When these weapons were openly worn, men were expected to be able to use them. Permission to carry these items stated plainly, “I am a fully enfranchised male in this culture and, as such, under certain culturally proscribed conditions, I have the right to kill another person”. Logically, this right also exposed the wearer to the possibility of the same fate. It follows that an item embodying these potentials and displayed so prominently as part of male dress would have all the craftsmanship and aesthetic beauty the culture could supply and the wearer could afford.
If you are asking whether or not the weapons collected are part of the cultural heritage of the individual collector, the answer is, in most cases, probably not. If however, you are asking if these weapons we collect are part of our cultural heritage as humans, then the answer is undeniably (for better or for worse) yes. Art transcends culture and the greater the art, the greater the transcendence. They are not just “big boys’ toys”. They are vitally important items of human material culture.

Sincerely,
RobT