Tunesmith, I wasn't going to reply. But, honestly, I believe you reflect the right-handed bias that runs deep in many cultures. I hope you can accept that I say that without malice. I really don't trust e-mail where tone matters.

There are left-handed violinists. Mostly, they are fiddlers or others who don't have to adapt to orchestral playing. I worked with such a fellow for years. Fortunately for him, he was also an instrument builder and repairman, so reworking the violin was not a big worry for him. He also played a custom LH martin D-28. Fortunately for the rest of the band, he was the kind of player you can absolutely always count on.

Come to that, look at some of the old photos of groups of irish uillean pipers from the turn of the last century. You'll find the occasional left-handed pipe set. Pretty weird-lookin', even to me. I play winds right-handed BTW. Never seen a LH clarinet or sax.
But there are whistle players and fifers who reverse hands.

If one wants to play violin in an orchestra one has no choice, given the way orchestras operate. And, yes, some naturally left-handed people adapt very well to right-handed playing. It is just that others do not, and that in many situations there is no reason to pressure them to do so.

But turn it around. If it really makes no difference which way you play an instrument on which both hands are necessary, borrow a left-handed version of your favorite instrument and play it for a while. Shouldn't be that hard, should it ?

And please (!!!), if you ever find a left-handed ice cream scoop (the kind with a thumb lever on the side that opearates a scraper inside the bowl) let me know.

Yours in diversity,   - George