Yeah the game requires you to pick a faction to do the main quest. Plus it is the best way to boost your levels, just wandering alone, shooting raiders and what not won't get it done.
Yes, and I do that partially. I'm level 33 or so now and die mostly only because I got too cocky / lazy. Now I'm basically following the main quest only with the additional side-quest presented by characters I like (Hancock or Nick for example).
I just think it's missing a "faction" where you mind mostly your own business or where you actually create the faction. Let's call it "The Good Guys". Now you have a really nice Open World with pretty good choices how to tackle the game with lots of freedom but ultimately and unavoidably get pushed into tunnel vision of those faction quests. Just a minor nickpick maybe but definitely missing that!