The zero fret is theoretically a solution (best implemented in manufacturing rather than retrofitted), but it's curious that several zero fret guitars utilize a zero fret that's larger than the rest. Which kind of negates the biggest theoretical advantage they have. I'm guessing that designers of such instruments think players expect/prefer open strings to have higher action than the rest of the frets. Which is a little baffling to me, but whatever...
Compensated nuts are a thing people use and sometimes like, but they're really best if you are one of those people who prefer open strings to have higher action. If you like the action at the nut to be set as low as a fret, they offer no real advantage. Unless the nut isn't properly placed...
...which can be the case. I've occasionally seen a nut creep away from the fingerboard, which would exacerbate any sharp notes. There's also the possibility that the nut is set too close to the bridge overall, due to the fingerboard end being cut as if for a fret, where the theoretical placement of the nut doesn't take into account the kerf of the saw. This would be a pretty minuscule error, but the error would probably make it generally perform more in tune with the nut action being on the high side.
It is funny overall how common this problem is on guitars across a pretty wide spectrum of quality, price, and reputation. It always bugged the hell out of me how often this is done wrong.
Compensated nuts are a thing people use and sometimes like, but they're really best if you are one of those people who prefer open strings to have higher action. If you like the action at the nut to be set as low as a fret, they offer no real advantage. Unless the nut isn't properly placed...
...which can be the case. I've occasionally seen a nut creep away from the fingerboard, which would exacerbate any sharp notes. There's also the possibility that the nut is set too close to the bridge overall, due to the fingerboard end being cut as if for a fret, where the theoretical placement of the nut doesn't take into account the kerf of the saw. This would be a pretty minuscule error, but the error would probably make it generally perform more in tune with the nut action being on the high side.
It is funny overall how common this problem is on guitars across a pretty wide spectrum of quality, price, and reputation. It always bugged the hell out of me how often this is done wrong.