There's nothing wrong with repetition, and there's nothing wrong with being innovative. Not unto themselves, anyway.
The big question is what you do with the Predator franchise. Anthology style stories is not a bad idea on its own. BUT. As someone pointed out, if all you're doing is moving from time period to time period with a Predator hunting dudes... No, that's a terrible idea. The novelty cannot carry it for the whole of the film. You might get away with that once, but after that you'll really need to do some things to make it new and exciting. There are baseline tropes you could use to setup each story differently. For example, one thing in the fan film Predator Dark Ages that is used to at least give it some difference to the original film is the use of conflict between Christian Crusaders and the Saracen warrior. You could build a series of films around tropes like that. An adventure film, a story of an aging warrior, coming of age, finding the way home. Etc, but you'd need some really incredible writing to make it fresh. Otherwise you just end up with another predator killing another group of people.
I always held the first Predator film in much higher regard than just another slasher film, and that's what an anthology series of films runs the risk of doing. The first Predator has great writing, acting, music, pacing, a great villain, and it has one of the most subtle and glorious genre twists in cinema history. It's a horror movie with macho men who think they're in an action movie. The whole thing is about learning to think like the beast. To be the animal.
You can't just repeat that, and for as much as Predator 2 tries to move the goal posts into cop movie territory, let's be real. Predator 2 is still a messy movie. It's better than it was ever given credit for, sure, but it is messy. When compared to the first film, which is this really streamlined, well-oiled machine that starts and doesn't stop. It just keeps the tension going.
An example of what an anthology could look like, we have already seen attempted in the fan community with "Untitled Predator Film" "Warrior : Predator" "Predator Celtic Days" and "Predator Dark Ages." That's four different time periods...
That's all they really do though is change the time period. The musical cues are more or less the same, dialogue is copied and pasted. Granted I think Dark Ages did a reasonably good job of incorporating the time period into the story, it still suffered from fan-fiction-itus where you have to quote the original in place of writing your own dialogue.
And then we run the risk of going into silly territory. Predators popping up in Caveman era, or fighting dinosaurs, or Nazis... Does the series then have any credibility left?
Does it have any credibility left right now after The Predator for that matter? I felt the series died the moment I read the script. Which, everyone at the time was saying "You can't judge it by the script!" Well... Yeah, you can. It didn't read any better than it played, and nothing significant was changed or fixed. It did critical damage to the series.
I mean, do future films just ignore The Predator? And when you set that precedent... Well, you start down the path of the Terminator franchise which has done so many left and rights with the continuity who knows what is or isn't important to the story being told.
Let's go with the idea of doing a soft-reboot. I think Hicks is right, they should tackle the Bad Blood concept head on. What I would do is have a film that starts very similar to the first Predator. Spec Ops team, maybe a group like Soldier of Fortune or the Expendables so you can have an international group of badasses... They go some place hot and full of conflict. So, similar beats to Predator, and then just when you think you've got the plot nailed down there's another Predator that shows up and you find out a lot of the slaughtering going on was Predator B, not Predator A. The nature of things changes at that point because now the characters are literally caught in this storm of two beasts going at it.
The Predator basically screwed up my basis for a Predator film universe. By way of using OWLF I figured there was a way to setup a series of films that had humanity go from victim/prey to re-balancing and turning the tables on the Predators. Alas The Predator took those ideas, did them really crappy, and wiped their ass with the blank pages to fill it in.