It seems to me that whoever first designed the guitar thought “hm, I’ll make it so that you can only reach up to about the 13th or 14th fred, but I’ll make it have 18 or 20 just to tease you!”
Really, why don’t all guitars, acoustic or electric, have cuttaways? Does it affect the tone? Does it make construction that much harder? Is it just tradition?
It’s up to the player. Some like them, some don’t. My electric guitar has a cutaway, my acoustic doesn’t. Almost all electric guitars have them because you need access to the higher frets. Acoustic guitar players usually don’t play up there (but some do, see dave mathews/john mayer school of guitar).
There’s also the matter of intonation. On an electric guitar, the bridge tends to be much more adjustable than the 1- or 2-saddle design of most acoustic guitars. That means that it’s more likely for an electric guitar to be in tune at the top of the neck than for an acoustic guitar.
I do own a Mexican requinto (a small, nylon-string guitar) that has a cutout and is fretted right up to the soundhole. The intonation at the top of the neck leaves something to be desired.
I may be talking completely out of my ass here (I know there are more knowlegeable doper guitarists out there), but I’m thinking in earlier times, the part of the fretboard that overlapped onto the body was considered kinda sorta cosmetic. And I reckon folks didn’t usually play that far up the neck back then.
(Actually, I’d bet back then the bigger problem back then would be that the strings would be like half a freakin’ inch above the fretboard up there and that was a bigger PITA than reaching around the body.)
Basically, the neck overlapped onto the body as part of the design. If the fretboard only went to the point where the neck meets the body, what do you do with the part of the neck that’s overlapping the body? The continuity would be broken if you finished it like the top (body). Then they probably left it that way because “that’s the way we’ve always done it/that’s the way everybody else does it”.
Then players came along who could actually play up there and designs improved, and so on.
There are some good reasons to have no cutaway. It’s cheaper to go that way; there’s less joinery and bracing. It’s for the sound, too. The guitar’s voice depends on the size and shape of that wooden box. If you take away a big chunk behind the high pitched strings, you make them quieter than they already are, and you also cut down on the overall size of the sound box.
On a solid body, the shape and size of the body matters very little. Johnny Winter played one with no headstock (the tuners were at the bridge end) and just enough body to hold the controls. There was even one freakish model with such an extreme cutaway that there was just air under the strings at the end of the fretboard. There was a cantilever from the top of the body to one side of the neck.