The whole point of rebooting something is to be able to bring fresh ideas into the system, which can include stories or mechanics. At the very least a sequel should have some kind of feature parity with the first game, otherwise you've essentially just made a shitty DLC as the next iteration by dropping features.

Saint's Row 2 had a great amount of content, and even when we were playing over LAN with Hamachi, the game was somehow smart enough to figure out what stupid shit we were getting up to, and it prompted us to play "death tag". We didn't even know it was a built in feature in the game, we had just been running around killing each other in various funny ways until the game said "hey, we have a structured way you can do this" and we had a blast.

Saint's Row 3 expanded on everything SR2 had set up. It drove the story forward, the engine was much better than the original PS2 iteration and there were just as many minigames if not more.

Saint's Row 4 took everything to the extreme though, which is unfortunate because that's really where the death starts happening. When they literally blew up the planet as a plot point and turned it into a Matrix parody it lost a ton of focus and grounding that made it enjoyable long-term.