Well, I can't argue with your points about GTA 3.
Saints Row 3 has similar mechanics, but it's
really quite goofy compared to 2. And 2 was already pretty silly compared to 1. I don't mean that getting goofier is better or worse, just different. Saints Row as a franchise has never really had a consistent, thematic approach. But what you're talking about, I suppose, is mechanics.
What this all comes down to is asking, "just what is a game franchise?". What does it
mean for a game (or a movie (or a breakfast cereal)) to be labelled "Mario", "Zelda", or "Saints Row"? At its barest, it means the company making it has the right to use the name, which is probably trademarked. Beyond that, there's usually either a thematic approach (a style), a set of characters, and/or game mechanics that are being re-used. And they often build on a story. Super Mario RPG shared characters and vague themes with other Mario games, but not mechanics at all. Majora's Mask and Wind Waker are nothing alike in style, but have very similar mechanics. Lords of Shadow uses completely different mechanics (yet similar to other games outside the franchise, and vaguely reminiscent of the 3D PS2 and N64 games), reuses yet overhauls the characters, and continues both the general thematic approach and the overall structure of the NES games (not so much the SotN era games). The only thing GTA3 has in common with previous games are some broad mechanics (driving cars) and the general structure of progression. I know you didn't like that, but a lot of folks enjoyed the new perspective.
What I'm saying is that there are several ways to make a game that's part of a franchise in more than just name, and they can be enjoyable if you take them for what they are rather than a betrayal of expectations that, really, you never should have had. What you're looking for is a game that "plays like Saints Row 2 and 3", which is fine, but that doesn't make the Saints Row Facebook strategy game (whatever it was) any less of a "Saints Row" game just because it is mechanically different. Read reviews. Know what you're getting into. You'll be better off for it.
The nice thing about mechanics is that they aren't copyrighted (except in the very strictest sense of making a nearly exact clone of an entire game). Any other game studio is free to create a game like Saints Row 2 and 3 without any sort of repercussion, aside from other gamers accusing them of "ripping off" another game (see Lords of Shadow and God of War, again). I almost wish someone would; I like there to be a wide variety of games out there to suit all tastes. It's just the limited nature of our capitalist market and finite population that we can't make all games at all times.