Depending on the nature of the flat, patch type, tube size, and tire/rim combination fixing a flat may be anywhere from easy to the most difficult bicycle repair task ever encountered. Hopefully we don't get a flats very often, so for whatever particular combination of patch kit, tube, tires, and rims I'm currently using it could take many years to find out whether the task will be easy or hard (not to mention the fact that the nature of the puncture could ultimately render the repair futile).

Not something I want to experiment with when I'm trying to get somewhere. Especially since even in the worst case one never has to travel more than half the total distance of the trip in order to delay the repair for a more convenient time; Although on average one shouldn't need to travel more than 1/4 of the total distance and it will probably take half that just to be completely sure you even have a flat. So let's say you're going on a 16 mile journey, if you flat on average you'll probably have to travel something like 4 miles to get to either the destination or origin, it will probably take 2 miles to be completely sure you have a flat, which leaves you stranded for only 2 miles. For those two miles IMO it makes more sense just to walk or ride on the rims; you probably won't be able to fix the flat faster especially when you consider all the things that could go wrong in attempting to do so.