[BeniBoy]

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.

[omnicognate]

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.

[omnicognate]

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".