I agree that George's early songs weren't brilliant-- but neither were Lennon/McCartney's. You've got to consider their pre-recording era songs as their "beginner" library-- not particularly inspiring. "Love Me Do" was their first hit and, I'm with George Martin on this one. I just don't like that song very much. Of course, I'm looking at it from the perspective of time. At the time, I understand the harmonica (GM's suggestion per Geoff Emerick) made the sound unique, and that's why it went as high as it did in the charts. GM also rearranged PPM from (his word) a "dirge" into the peppy happy song that we now know (and I really like). Notice GM kept the harmonica in all the early Beatles' songs-- that was their selling point and signature sound, as far as he was concerned.
GM did not put similar effort into shaping George's songs, by his own statements. So George was slower developing, and he didn't have the luxury of a songwriting partner to help craft his ideas, because Paul and John were the songwriting team and George wasn't. In the rush of Beatlemania, who else could he collaborate with, when most nights were in a completely different town and the only consistent people he had around them were his bandmates, who (again documented by GM) really didn't help George except to throw out a piece of advice here or there. He certainly learned a lot by watching, but crafting your own stuff takes some concentrated effort, and there just wasn't time available this, or effort expended by the others. When the touring stopped and George found himself with more time, he started composing a lot of songs. And some of those songs are among the Beatles' best and many people's favorites.
Anyway, I can see why many people think George wasn't crucial to the Beatles. I'll just say, he was for me. I wasn't motivated to buy any Beatles music until after watching the Anthology. I felt myself strongly relating to George, and so started investigating more into these Beatle people. It turned out, his songs were more to my taste-- a little more contemplative. Yes, the John and Paul hits were catchy, infectious, and I really enjoyed them-- but I didn't particularly need them in my house. I wanted George songs in my house. I'm in the minority, I realize. But I wouldn't be here if not for George, so I'm very grateful to him.