I used to voice the opinion the Time Lords were more interesting in their absence, and while there is a degree of truth to that statement, I'm not sure how much I meant it since when I got into classic Who the Time Lord centered stories were the ones I gravitated to first. Indeed, the first classic era story I watched was The Deadly Assassin.
Still, I don't really know what the Time Lords can really contribute to modern Who. There's really not much more you can do with them, they're corrupt bureaucratic douchebags, and while that can be fun to watch occasionally, there are more interesting aspects to the Who mythos. Then again, the first half of Hell Bent with all its Gallifrey drama was more interesting than the rest of the episode. Of course, the rest of Hell Bent was just the Doctor and Clara delivering monologues to each other, so there's not much of a competition there.
Still, I don't really know what the Time Lords can really contribute to modern Who. There's really not much more you can do with them, they're corrupt bureaucratic douchebags, and while that can be fun to watch occasionally, there are more interesting aspects to the Who mythos. Then again, the first half of Hell Bent with all its Gallifrey drama was more interesting than the rest of the episode. Of course, the rest of Hell Bent was just the Doctor and Clara delivering monologues to each other, so there's not much of a competition there.