I think that an amazing addition to Strava would be the addition of interval runs.
My idea is that when you click to record a run, you have the ability to choose to record a normal run or an interval run. That way, before you start your run, you could add intervals and when running you can completely focus on that instead of constantly looking at the time. Similarly like the sounds you get when entering a segment, you would hear a 'noise' to indicate the start of your interval. In addition to that, maybe the Strava voice could tell you what interval you're starting (for example, what heart zone you need to be in, what pace you have to run, ...).
I think this would be a great addition, because now when I'm doing intervals I'm constantly looking at my watch (and often forget my intervals).