I think both have their place. Songwriting is a skill as well as an art. Hardly anyone writes a great song their first time out. It takes practice. And in doing that practice, you're developing a bit of "theory," even if you may not know the technical musical term for it.
For example, you probably learn quickly which open chords tend to go together easily at first, such as G and C, or G and D, or E and A, or A and D---things like that. By doing that, you're discovering some basic rules of harmony.
I think writing "purely on instict" is impossible. You're always learning things based on past experience; whether or not you have a name for it isn't the point.
A lot of people say "I just start singing a random melody and then try to find chords that I like." Well, they may think that's what they're doing, but I don't think it really is. If you've listened to a lot of Western music growing up, which most of us probably have, then you're probably very familiar with musical concepts that get used over and over, like the major scale. I'm not saying you can notate it on a piece of paper, but you know what it sounds like, and you can imitate things you hear and even predict things because music is a langauge.
Common melodies are like sentences that get used all the time. If we hear the words "Oh well, that's the way it...", we can predict that most of the time, the next word is going to "goes." This familiarity extends to music too. We hear beginnings of certain stock melodies and can often predict where they're going to go, even if we have no musical "training" whatsoever.
Anyway, knowing "theory" is really just knowing labels for things. I can guarantee that, even though Paul or John may have not known the technical terms for the progressions they wrote, they weren't "writing blindly."
There's a great part of a Paul McCartney interview when he talks about one specific musical concept they learned. I can't remember the exact tune, but he was talking about the bridge. The song was in the key of C, and they went to
a G minor chord for the bridge.
I think it was "From Me to You." He specifically mentions that chord and how they thought "oh wow, we've never done this before!" They were using a minor v chord, which actually turned out to be a ii chord in a brief ii-V-I tonicization of IV. So the bridge went Gm - C - F, which is a ii-V-I in the key of F (the IV chord of of the original key, C)
The proof that they understood the musical concept being used here is that they did it in other songs
in other keys, like "I Wanna Hold Your Hand," where it showed up as a Dm-G-C progression in a song that's originally in the key of G. Same ii-V of IV relationship.
This is a great example of writers that couldn't read or write music, but they obviously had command of a great bit of music theory, even if they couldn't tell you the name of it.
Lots of people can speak English very well, but I'd say the majority of people can't diagram sentences as well.
