From a storytellng perspective, randos aren't that interesting because they're basically blank and disposable. I like the idea of defined characters with personalities, backgrounds, and agendas. If it's possible for your companions to also turn into your love interest, then it's more interesting if they aren't randos, otherwise you have a Skyrim-like situation where you're the only living thing in the entire world. I don't want to go through that again, so I'd like companions which are alive.
And Chris, if you're making the game boring by looking up a walkthrough, then that's not the game's fault.
Okay, but if the point is to "be surprised" by companion recruitment, then I'd rather have a system where it's possible to miss out on companions because of your choices. And perhaps getting a new person to your side opens up some other missions. That way you have something new to look forward to with each playthrough.
I gotta go with flash (ah-aaaaaahhhhhhhh) here pal. Random generated character just can't really have the kind of personality that would make them worthwhile....
I would much rather have a limited number of companions with choice personalities.... I mean Kinzie in SR3 was probably the best thing about the game (Other than the vtol, man that thing was sweet). I frickin loved that nerdy chick...
My alcoholic trader chick in Fallout New Vegas, or the Raoul, the ghoul cabarello in New Vegas.... the companions were memorable...
Now, that being said...
ALSO having the ability to just call up random dude or dudette to come be your backup, and if you like em letting em stay hired on... that would be kinda cool too...