Playing up and down on a single string is good. Position playing is also good.

Playing up and down on a single string is good for a number of reasons. The best one is: It sounds good. Each string has its own timbre, so if you play a melody on a single string the notes will sound more alike than if you play them on different strings.

The next best one is: It feels great. Just try it!

It's also good because the intervals are right there in front of you, all you have to do is look.

I think it's also easier to play spontaneously on a single-string than using positions, though that gets easier with practice.

By the way, it helps a lot to whistle, hum or sing when improvising or playing by ear. It makes it easier to hit the right notes, for some reason. I do this occasionally.

The ability to play on a single string is very useful when you have to (or want to) make a long jump and also for shifting positions.

Also, if a string breaks while you're playing, you can cope a lot better if you can play up and down single strings. If you only know to play using positions, you're in trouble.

One thing to try is playing an E major scale (or some other scale) _smoothly_ from the low end of the guitar up to the highest notes. It works best to shift a position or two at a time, instead of playing as much as possible in first position and then trying to get into a higher position in one go. And then back down, of course.

Playing up and down single strings (or several single strings, if you know what I mean) is the way melodies are usually played with a slide.

I usually play a mixture of positions and going up and down single strings. I don't really have to think about it anymore (though I do have to practice because I don't always hit the right notes).

Major scales are good because the chords built from the major scale are the basis of harmony. If you know the major scales inside and out, it's not very difficult to learn other scales. I find that it's not really necessary to learn dozens of other scales if you can play by ear. If you know the major scales and the various arpeggios, you will have already mastered this material. Constructing other scales is sort of just expressing the same things in a different way.

That is, if you know the major scales and the various possible alterations, flatted fifth, augmented fifth, minor third, etc., and are able to hear things in your head and play what you hear in your head on the guitar, you've got the information and the skills you need. Then, when you're playing, you can forget about positions, scales, argeggios and whatever. I'd heard this idea before, but it took me years before I got it.

People say you have to crawl before you can walk, but it is also true that if a person can already walk, or even run, you're not helping him by making him crawl, even if it's the newest, most modern, up-to-date method of crawling developed by an elite team of music educators.