Does the third working set add much to your workout?

I usually see exercises written as three sets of eight, ten or twelve repetitions, but I’ve been wondering how much the third set genuinely adds.

The first working set is often the strongest; the second still feels productive, but by the third the weight or reps may have dropped, and technique can start to deteriorate. Is that final set providing a useful extra stimulus, or mainly adding fatigue that you have to recover from?

Some people seem to progress perfectly well with two hard working sets per exercise, while others prefer three or four sets and feel they need the extra volume.

How many working sets do you normally perform, and have you ever reduced them without losing progress?

I imagine the answer also depends on how many exercises you do for the same muscle group. Three sets may make sense when it is your only chest exercise, for example, but perhaps less so after several presses and fly variations.

Has anyone found that two genuinely hard sets produced better results than three or four simply because the programme prescribed them?