Grant Morrison has said that he's more interested in Kyle than in any "classic" GL (or maybe it was Silver Age characters? I'm not sure), and it shows in his writing in JLA. He's out of place in the team, which is why he fits in so nicely in the book. Kyle was already interesting when Morrie picked him up, and Morrie made him even more interesting through team interaction.
Kyle being picked out from the street was a poor choice in the traditional sense, and certanly a poor choice for the universe he's supposed to protect, but as a story, it's an interesting choice and, along with Emerald Twilight, the most interesting thing to happen in the book since GL/GA in the 70's.

Ron Marz screwed up in the first four or so Kyle issues. Maybe he was drained from having to write Emerald Twilight so quickly, but the fact is that he didn't execute what was an excellent idea very well: the concept was to set a status quo with Kyle and his on-off girlfriend/semi-sidekick Alex fighting crime in California, and then fuck up the quo by having Alex killed because Kyle is GL, and have Kyle move to NY. He failed in making the story interesting and making the concept clear. However, after that the book had quite a nice moment, with Kyle actually learning and developing relationships with the rest of the DCU, including Hal. The first space adventure, the first meeting with a super team, a long series of fuck ups (the more I think about it, the more fuck ups I find, and these are obviously intentional on Marz's part)... these are things you don't see in other books, because they just magically happen from one moment to the other. If anything, they're shown as lame retroactive "Year One" type stories set in gray areas of the character's past.

I can understand why most GL fans didn't like Marz's run: the book had nothing to do with the Green Lantern concept. It was a book about the superhero world and the making of a superhero from scratch.