The origins of the guitar lie in African instruments comprising a gourd, a stick and a single string. All of the complexity lies in the plucking rhythm. This evolved into bowed instruments for more volume and expression and any violinist will tell you how difficult bowing is, and multi-string fretted instruments like the lute.

Some lutes can have 17 or more strings, some unfretted, played harp-like and the remainder (played on a fretted neck) are tuned very close together, so most of the playing complexity lies in the picking hand.

As a left-handed guitar player for nearly 30 years, I would confirm that the complexity in the playing lies in the picking hand (or occasionally the teeth, in the case of Jimi Hendrix, probably the most famous left-handed guitar player).

It is generally believed that one can play either handed instrument if one learns that way (I simply picked one up left-handed and went from there) - Mark Knopfler, for example, is left handed but plays a right-handed instrument.

As someone who can play a guitar in the normal way, or upside down, with my hands doing 'opposite' jobs, I think this is down to the fact that in the normal position, the left hand doesn't need to be nearly as precise as the right.  The left hand moves 'outside of the rhythm' of the music, fretting pre-ordained shapes and patterns.  The right hand must be much more flexible, adjusting it's rhythm to match that of the drums and bass guitar.  If the right hand makes an error, it usually sounds terrible, as the notes are played out of time.  If a mistake is made by the left hand, while potentially out of tune, the note is drowned by up to five other notes, and the other instruments that play notes or beats at the same time.

Interestingly, a run down of many great guitarists reveals an unnatural amount of lefties - Hendrix, Cobain, McCartney, Easton, King, Dale, Rush, Armstrong, McKay, Iommi, Rosas, Rhys, Campbell, White, Geldof, Seal, Womack, Thomas, Michael Angelo Batio, Dangerfield, Harcourt, and Pop are all of a left handed persuasion.

Handedness is related to language dominance.

In most people the left hemisphere of the brain is dominant for language. As the right side of the body is controlled by the left hemisphere it is the right hand/arm in the majority of people that deals with aspects of communication such as writing and communicative gesture. When playing a stringed instrument it is the hand that strums, plucks or bows that is the 'voice' of the player. The hand that stops the strings to create pitch can not easily make a sound on it's own. Though the action of the pitch creating hand is complex, it's action is more akin to the role the left hand of a right-handed person plays when writing, that of holding and steadying the instrument of communication.

Not all left handers show language dominance in their right hemisphere. A study done by the Department of Neurology, University of Munster, Germany found that in extreme left-handers the incidence of right-hemisphere language dominance was 27%, whereas in extreme right-handers it was 4%. As playing a string instrument does lead to a degree of learned ambidextrousness it is possibly only the left handed musicians with right hemisphere language dominance who feel the need to customize their instrument to a mirror of the traditional right-handed set up.

Speaking as a long time right handed electric guitarist only, the right hand is largely responsible for fine controlling the tone and feel of notes played, not just their duration,via muting,the use of the pick to generate harmonics, and a lot of other techniques. It's very important as a control mechanism. I'd imagine something of the same reasoning for a bowed instrument, the necessity for fine control going to the strong hand.

However, as you note, some like Macca do play using their ''strong'' hand as the control/picking/strumming hand, although I'd guess that may be at least partly down to the lesser availability & expense of proper left handers when he was learning to play (not so much of a problem now) & just stuck with what he's used to, although to take a counter example, Hendrix used right handed guitars converted to play left (tipped upside down!).

This is not an answer as such just an observation. Our 8 year old left handed son began to play the guitar as a right handed player but as soon as we restrung the strings for his left hand he was much happier and made much more progress ,obviously he naturally prefers this set up. On a random but slightly related point, he was very happy to find out from one of his many fact books " that he was not alone~ polar bears are left handed too!" ~ (not sure what their take on guitar playing is.......)