It's usually not a good idea to tune a guitar as you described. Basically a guitar has to use "temperate tuning" because it has frets, so you can't be absolutely in tune everywhere, but you can minimize the error on each position. So if you tune string by string relying on fretting the last string, you will "carry" the error, and the resulting tuning will be wrong. It is good for a first pass, but you then want to check that some specific positions do sound good. Depending on what you are playing (for example if you rely more on some open chord position), you might even want to tune the open string to make those position sound especially good (at the expense of some less common one). That is commonly referred to as "sweetened tuning".

EDIT: I might have confused things indeed. If you fret, you should not carry the error. Usually, an practical way to tune two string is to play harmonics and listen to the "beats" between them. That will carry the error. Fretting should work, but in practice does not really because that suppose that your intonation is perfect (ie the fret are perfectly placed), which they usually are not, especially on acoustics with no easy way to set it up.

That's very interesting. The tuning for a violin is always (afaik) to make the open strings a perfect 3/2 fifth apart, but then of course you can play to whatever tuning you want. (If you have the skill to do that - I certainly don't!)

That makes tuning a guitar a much more complex thing in principle, with choices and trade-offs to be made, so maybe that's a better explanation for the prevalence of tuners.

I say "always" (for the violin), but that has problems itself. Eg. If you're playing with an equal temperament (eg piano) accompaniment your open G will not match it and there's no other way to play that note. Presumably advanced violinists have to choose their own tradeoffs, but I was always taught to hear the fifth and would always be aiming for a just fifth (tuning an equal tempered fifth by ear would be a neat trick!).

Edit: Hmmm, thinking about it the guitar should be easier to tune to equal temperament (if that's what you want) as presumably the frets are equal-temperament semitones apart. For that tuning, it's the violinist who's "carrying the error".

On the cello (and viola) three perfect 3:2 ("pythagorian") fifths down from the A string makes for a low C that's noticeably flat when compared to equal-tempered instruments. For string quartet playing, it's manageable, because the violins will adjust when necessary, but for piano-accompanied playing, cellists will raise the low C a little so it doesn't clash with the C's on the piano.

> presumably the frets are equal-temperament semitones apart

Guitars are made of wood, which bends (both the neck and the top) as one adjusts the tension of the strings. As the neck bends, the length of the string between the bridge and nut changes, and the height of the strings above the fingerboard varies in quite a complex way along the neck, changing the amount of tension added by pushing the string down to hold it against the fret. Similar changes in frequency occur as frets and fretboard wear down a little, increasing the distance needed to properly fret a string.

The neck and top will warp and bend with age, with changes in temperature and humidity. And after a guitar has been played a while, it will have been worked over by one or more guitar technicians. There are so many variables that nothing can be taken for granted. Using accurate electronic tuners is presumably the simplest and fastest way for guitarists to maintain respectable pitch in most musical presentations.

Guitars have a neck tension rod with an adjustment screw that changes the neck bow. They also have intonation adjustment screws that adjust the location of the tail bridge for each string individually. Then there's still tail bridge string height adjustment.

Neck adjustment needs to be done because seasonal moisture changes can change the bow of the neck. Depends on guitar. This is mostly for proper playing action, so strings don't buzz but aren't too high from the fret board either.

Intonation needs to be changed when you change some other things, like the things mentioned above or string gauge for example. There a tuner is very handy, you can compare the string fretted on the twelvth fret to its harmonic there. The differences are small and hard to hear.

Same things apply for electric basses.

Don't know how things are dealt with on a violin or cello, but the lack of frets certainly makes some of the adjustments unneeded.

With guitar, you only adjust these things when doing maintenance, not in the back room and certainly not on stage.