I suppose I do enjoy some drama. I like the game feel high stakes for the players (and characters) but I am more interested in Cinematic Style play anymore. Even my horror games are a little more Cinematic than they are Gritty Dramatic.
Just the other night my wife and I were talking Power Creep in games and TV shows and how to prevent it from being a series killer. Shows like Grimm, or Buffy, tend only to last 6 or 7 seasons because you have to keep upping the ante on the power to increase the drama. Fight a vampire Season 1, you need a demon Season 2, a God Season 3 and then...oops. Too far too fast. Star Trek TNG had the same problem, once you introduce the Borg where is up?
Shows like X-Files and Supernatural have to come up with ways to justify what is going on. In X-Files' case, I think the show fell apart under its own weight. Supernatural...they just keep doing their own thing and the audience is happy. In the case of X-Files, the drama got too much. In Supernatural, it didn't.
But in the case of Supernatural, the drama hasn't changed, it just gets reused. Certainly not the melodrama. In Arrow, also mostly normal humans, the drama had to come from strained interpersonal relations that were supposedly solved in the previous seasons. Which is the same thing the next season. While it has worked, one can argue, for Supernatural, it didn't as much for Arrow.
On the other end of the spectrum, you can have games like old-school D&D.
People will often claim that old-school D&D doesn't have, or shouldn't have drama. I say people are missing out. I often prefer more cinematic play in my D&D as well, but there is still room for some drama. Of course, D&D is not like a TV show. There is always something more powerful. And thus the Power Creep. We see as the levels go on and even as the editions go on. I did my analysis a while back where I showed a 1st level D&D 4 character was as powerful as a 6th level BECMI character. The monsters accordingly so as well.
Can you increase drama without power creep? Sure. But you have to be careful about it.