> The worst for me is when they catch the breakaway mere miles from the finish line. Sometimes a person stays away all day only to end up finishing in the group, or at least beaten by all the sprinters.

Yeah, this is why I (and most others, I believe) find most of the sprint stages in the Tour pretty boring. The break vs. peloton dynamic is critical for road races to work (e.g. if there's no one up the road, why don't we all just ride along at 25kph?), but in those flat stages, the sprint teams are so good and care so much about the sprint finish that it's almost a guarantee they catch the break.