The browser is the time-sink for me too. Unfortunately, iOS makes it difficult to get Safari out of your life. My dream is a content blocker that requires you to unlock it in order to browse the time-sink sites you choose to greylist; and each time you unlock it, unlocking gets more arduous.
Thing is, I don't want to block it entirely. Sometimes you just need to look stuff up. Just limit time spent on time suck sites. The real problem is that there's no way to tell the OS to open links from other apps into a different browser that you can add better controls to.
