Is there any reason given why an advanced alien species that can fly literally anywhere in space would need take Earth, or is it another "They're coming for our entirely common resources they could find any of a trillion other places" story? I think someone said they were coming here because our planet is heating up while theirs is cooling?
Yes, I said that. It's also said they keep coming back
because we're an endangered species - they're getting supplies while they last. I can't recall if it's fully explicated but I believe it's the newer/possibly dominant faction that embarked on the plan to take Earth as well. It's made clear they hunt to hybridize and improve themselves - hence the reason the term 'predator' is used when actual predators, strictly speaking, do not hunt for sport (this issue is an ongoing point in the script and leads to the later reveal) - but now that hybridization has a new purpose, namely allowing them to acclimate to our relatively nearby world which is approaching hothouse conditions which suit their species. This part is made clear.
As for why they don't go to some other hot planet - because it's a movie franchise, and because there is no money in 'Predators go to entirely new planet with no humans involved'. Though I wouldn't be surprised if we went to theirs in a future sequel.
It also changes the whole plot of hunting and randers other film nonexistent.
But why war in first place? It's one of the very few that successfully tried something different and now it's going back to 'they want our planet, let's fight back!'.
It doesn't render those films nonexistent; they happened. But this story draws a much clearer distinction between the concept of hunter and Predator and gets into why they hunt for sport as opposed to being strictly natural predators. Also, this is not leading to the kind of movie you are thinking of. In terms of how the Predators behave in this story, regardless of what their strategy is, their execution is what it has always been - kill everything.
As for trying something different, this is that. Not trying something different would be making another variation on the movie from '87, another straight hunt. Predators
tried that and flopped. This story gives the franchise an aim and future purpose. Whether you dig it or not is up to you when you see the movie.