Re: Why are left and right handed guitars seemingly backwards?
The lute was intended for both melody and rhythm, with an expanded vocabulary over the lyre, from which it derived. That's why lutes had frets. As the guitar is derived from the lute ("luthier" being the word for "one who makes lutes), it was also intended for both rhythm and melody. However, cork-sniffers relegated it to rhythm largely due to its limited range compared to a traditional piano or clavinet or harpsichord. Very few top-name composers wrote specifically for the guitar, and fewer still wrote for all-guitar ensembles.
As for the fretting hand doing more work, in classical compositions, the picking hand actually does more work while the fretting hand holds shapes which facilitate chords, scales, and arpeggios picked by the picking hand using all 5 fingers. Alternate tunings were devised to allow a single finger to hold a full chord shape while leaving the other 3 fretting fingers to play more technical passages, similar to a violin, and to do more complex, additive chords, though some alternate tunings made diminished chords more difficult.
As well, a single guitar was able to provide both rhythm and melody simultaneously, which only the piano and its like could do.
Typically, the fretting hand did not do single-string patterns using multiple fingers. That came along in the Jazz era when guitarists would play horn lines, either to substitute for a horn or to double it when a second horn player was unavailable. This led to the invention of the electromagnetic pickup and amplifier. The single-string technique was then adopted by Blues players for the same reason.
Since the guitar was already established by the time Jazz and Rock came along, guitars were still being made according to the principles of Classical-era guitars and lutes, where the fretting hand was the off-hand and the picking hand was the dominant. When plectrums as used by the Greek bouzouki or Russian balalaika and other similar versions of the lute and guitar were adopted by Jazz guitarists (as opposed to strumming with the thumb or traditional Classical 5-finger techniques), this further moved the picking hand to one of basic motion, while the fretting-hand became the primary melody-maker.
So, your observation is correct: if you're right-handed, you should play a left-handed guitar, and will most likely develop on it faster than forcing your off-hand to be more articulate, while training your dominant hand to be less articulate.
Pianos are typically made so the right hand (melody) does more work than the left (rhythm). Some left-handed players have custom-made left-handed pianos. I've always wondered if high-end electronic keyboards have an option to flip the keys for this very reason.
This can be done easily for other stringed instruments, like violin and cello, simply by stringing them inversely.
We often see lefty drummers set their kits up " backwards" (Phil Collins).
Do left-handed players prefer left-footed pedal boards?