The idea was that the three week pieces add up to the whole of the larger task. (Yeah, I know - only if you didn't miss anything. Take the time to think it through well enough that you don't do that. And what if you have things you don't know? Then you have to do a research project to find them out before you can give valid estimates.)
"And what if you have things you don't know?" I usually find stuff out in the middle of work - a question comes up I don't have an answer for, and many times, no one else does either. In effect, no one can estimate it, but we didn't even know that up front. And... I've often hit things where the time to give an 'accurate' estimate takes more time than the actual work effort. Is that common in your "limit everything to 3 weeks" world?
If the time to give a more accurate estimate takes more time than the actual work, you aren't dealing with an estimate longer than three weeks. If the estimate is less than a day, it's not worth getting more precise.
To your first point: Yes, that happens sometimes. When it does, your estimates can be wrong. (Hey, they're estimates - they're not prophecies.) If that happens very often, though, you might add a fudge factor for "that kind of thing". Maybe something like "unknown surprises crop up most of the time, and when they do, they take about 20% of the effort, so we'll make our best estimate, then add 20%". That won't be perfect either - sometimes it will be 40%, and sometimes 0. But, you know, estimates...
