Bow marks aren’t there for synchronicity; up-bows and down-bows speak differently. Basically, because the frog–the part that the hair connects to near the player’s hand–allows for more pressure than the tip, a down-bow is used for downbeats and accents, as well as decrescendos, whereas an up-bow works well for upbeats and crescendos.
It’s nice when everyone’s bowing together, but the sound is the primary consideration.
I have seen and heard a lefty fiddle player. Lefty fiddle player in the sense of fiddle under opposite side of chin, etc.
The choir’s resident violin expert suggested that she was probably self-taught or possibly there was some kind of physical issue. Violin expert was a real wet-blanket on the subject.
The advantage of playing fiddle (vs. violin) lefty is that there tends to be only one fiddle player in a group (as opposed to a whole group of violins in an orchestra).
I played in a band briefly with a lefty violinist. Bowed with his left hand, held the strings with his right. I’ve never seen another in real life.
I am a guitarist, and I know a few lefty guitarists, including at least one who literally could not play right-handed. Paul McCartney is probably the best-known lefty player who couldn’t get the hang of guitar until he flipped it and reversed the strings. Some players are like that; playing lefty comes naturally, playing righty doesn’t.
With classically trained violinists, if you can’t get the hang of playing right handed, you don’t flip the instrument, you just don’t progress on it and eventually you are forced to give up.
In order to successfully play a violin lefty, the entire instrument would have to be a mirror image of a traditional instrument. You can’t just pick up a violin as is, and play it reversed, it just wouldn’t work. The strings, bridge, sound post and chin rest would have to be reversed, plus all the subtle asymmetries (including the bow). Then, of course, the instrument would be angled differently, so the sound would be projected toward the left.
If anything, it’s the viola that should be a lefty string instrument. It’s normally on the right side of the orchestra (from the audience’s point of view), so the sound is projected away from the audience. No wonder it’s so hard to hear them.
I’m a left-handed guitarist of forty years experience. I’ve also done a lot of teaching over the years. Lefty guitarists notice each other. I would estimate the number of fellow southpaw pickers I’ve seen over the years at around 1%, if that. Wikipedia claims that 87% to 92% of the population is right handed, so 8% to 13% is left handed. Assuming that the population of guitarists mirrors the general population in handedness, this would mean that only 8% to 12% of left handed guitarists play left handed.
Others have answered this question better than I could, but my impression was based on the fact that left-handed people are quite common but left-handed instruments are not.
I have only dabbled among musicians, but I know guitarists who are left-handed but barring a handful of notable celebrities, left-handed guitars are not often seen in the wild.
Spoken like a true right-handed person who has not been confronted with a world full of devices that are designed to be used by one’s non-dominant hand. I venture that you have no fucking idea what it’s like to constantly have to use things that do not fall naturally to your grasp and that require awkward positions and motions to manipulate. There are reasons why some left-handers choose to play a lefty guitar, regardless of whether it makes sense to your perspective.
Gary T, player of a left-handed guitar who found holding a guitar in the right-handed position to feel incredibly awkward and unnatural, to the point where it was worth putting up with the disadvantages.
Muppet musicians are usually lefties. But fiddle/violin players are uncommon.
Here’s a video that has both a lefty and a righty fiddle player. Oddly, it’s the Devil who isn’t “sinister”.
When I started this thread, I wasn’t thinking about guitars, though I knew there were LH guitars. When I made a futile stab at learning the guitar, it seemed to me the whole thing was backward. I’m right-handed, and my clumsier left hand had a hard time with all that complicated fretwork. In contrast, picking seemed much simpler.
Spoken like someone who couldn’t see past the chip on his shoulder to actually understand what I wrote. Better luck next time. 
As a guitarist, I would say: do whatever keeps you playing. If you are a “full lefty” like GaryT or FU Shakespeare, play left handed, period. If, however, you are on the ambi spectrum and could play Righty you might consider it, only to have access to ,ore selection. I see far fewer lefty players than statistics would indicate, I assume because they made that choice.
What I have observed.
As someone who plays string instruments as well as guitar . . . there’s a huge difference between bowing and picking. Bowing requires much more power and nuance and control than picking. And “complicated fretwork”? You’re lucky you have frets.
panache - ooo, very cool; ignorance being fought. I would appreciate hearing more about that. Do violins really require maintaining hand dominance? An interesting topic.
I see the points you share about bowing. I am not sure that translates to “harder.” I have transitioned to full fingerstyle on acoustic. The polyphonic, contrapuntal approach - oy: I have multiple strings going, with bass stuff and melody/chord stuff happening against each other. Mark Knopfler-Type stuff - when I get that going, I’ve got a lot of neurons firing, my friend ;)! And if the groove involves a steady bass thunk, my thumb feels like it’s running a marathon; not the same type of strength as bowing, I assume, but it requires building up endurance and strength for sure. Interesting.
Frets - my assumption is yeah, fretless is harder, hands down. I suspect some fretted techniques are equivalently hard at the Artist level of play, but fretless is so much harder at the most basic “play a note in tune” level.
Guitar player since 1973; fingerpicker since 1978; violinist since 2002. Panache speaks the truth! 
Bassist here, but similar situation. As a natural lefty I might have played left-handed but (in youthful ignorance) never imagined that there might even be such a thing as a ‘lefty’ bass guitar. :smack:
I learned string bass for a few years in middle school orchestra and I felt similarly as I am pretty much entirely left-dominant and trying to imagine fretting with a left hand as stupid as my right hand is seemed like an exercise in frustration and futility.
That being said, I was pretty terrible at string bass.