I think the interesting thing about the Saints series is that it really hasn't ever been the same thing twice. Sure there were similarities, and the overall genre was the same, but it really hasn't ever been real keen on true sequels. This of course leads to the ridiculous rifts in the fanbase with the SR2 crowd being high and mighty and what not, but putting that aside, I think that's a fantastic thing.
Other games tend to just do the same thing but different, or in a different place. The Elder Scrolls, for example, is basically just the same game with upgraded graphics and streamlined systems as time goes on. Saints Row, though? It always feels like a new game. For good or for ill, that was always neat to me, and I'd like to see more games actually do something similar. Doesn't look too likely though, what with every IP and it's mother being treated like a TV show series these days. Literally the only other IP that seems to be doing something similar is Bioware's Dragon Age, but I'm pretty sure that's unintentional.
IDK it's just cool. I really love all four of the games for different reasons, but I can see how their wild deviations might put a ton of people off, especially when we're used to sequels being essentially the same thing plus some extra shit, instead of new takes on the old formulas.