My last 2 games I've waited until the industrial or modern era to "expand". I was surprised how little diplo hit I took for even taking large numbers of cities and wonders. I try not to fully eliminate a civ, I leave them a garbage city. But in my Mali game, I did fully eliminate 2 civs, and I was still able to maintain my alliances.
This is weird to me because I feel like if I eliminate 2 or 3 civs early in the game, I take more of a diplo penalty, which shouldn't be the case based on how the game mechanics work (grievances fade away over the eras). Based on what I can tell, eras of friendly relations are overriding the grievances towards other players penalty when I check the relations tab in the diplo menu. So I'm able to keep all my alliances and friendships.
I may start doing more future games like this. Like I said, I did it in my Mali game, and my current Cleopatra game as well. The downside is you get some terrible district and wonder placement by the AI you inherit. I kind of had to do it in my Mali game due to my low production, and how hard it is to get that Civ up off the ground.