I like most of what you said here, but I personally can't stand fuzzy clocks with no mechanism to recover the loss of precision.

Sometimes I do actually want to know more about when it was, exactly. For instance, when I'm comparing things it would be nice if I could get actual timestamps instead of a bunch of things that say "about three hours ago".

So... I think I'm all for this thing right up to the point where I actually lose data because of it. If you replace my data with a more nice and simple way to say that, I'm even okay with that, so long as there's a way I can get the original data if I need it.