How does the number of strings on a guitar matter?
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From a playing perspective, on top of the answers here: The range of your standard 6-string guitar in standard tuning (EADGBe) from any root position/fingering position (4 frets wide, one fret for each finger) is two octaves. That could be 2 octaves in the key of F (first position) or key of G (3rd position), etc. Because the fingering for whatever scale is going to be the same no matter the root position, you can easily pick out notes and chords. This is especially useful because a guitarist can keep the same fingering position and execute key changes or different chords simply by moving their positioning up and down the neck.
However, there’s a design flaw that befalls every fretted string instrument: intonation. This means tuning an instrument to itself. The sign of proper intonation is if the 12th fret (the octive) gives you the same note as an open position. But this is a very fine measurement to get right, and it’s applied across 6 stings of varying length and gauge (thickness) so it is *very* difficult to get *almost* right, and pretty much impossible to get perfect. It’s why if you ever look at the bridge of electric guitars, you’ll see the saddle for each string is adjustable so as to assist with intonation. But again, your frets are the same size for each string at each position as opposed to being tailored to each string’s individual intonation. Therefore, your notes won’t always be 100% accurate. It’s less noticable for 6 strings across the neck than it would be for 9 individually tuned strings (12 string guitars are 6 pairs of the same note, so it’s pretty much the same as intonating a 6 string. And 7 strings have an additional 5 semi tones of bass under the low E string, so it’s not as noticeable as it’s mainly utilized lower down the neck).
There’s also a matter of action: the height of the strings from the neck. You want enough high action that you can fret a note and other frets won’t interfere (buzzing) and this can be caused by a variety of things: bridge height, nut height, ambient temperature, humidity/moisture, string tension, and truss tension. Inside the neck of most guitars is an adjustable truss rod that’s mainly meant to counteract string tension to prevent the neck from warping. More strings = more tension. More tension = more counter tension needed from the truss rod. It’s basically baked into the design of the instrument, and deviating from that design can cause problems with its playability over time. That’s not to say there aren’t exceptions to the rule when it comes to a custom design. But for your standard mass-produced and iconic instruments (stratocasters, jazzmasters, flying V’s Explorers, whatever), the math and engineering have been templated, and it’s just easier for the manufacturer.
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