I agree Richard C10. Up to a point. That is probably how you would like to analyse the satellite data and model the possible tracks. As a purely scientific exercise.
However real life is always more messy, and there were many other factors and agendas going on.
1. Inmarsat was breaking new ground here. The BTO analysis came out first, and this data was easily understood and was presumably readily accepted. So we had the north and the south arcs. The south arc was initially seen as more likely as no one (especially India) had observed the plane over the northern arc.
2. As soon as the south Indian ocean was identified as a possible area, everyone with a satellite started finding debris.
3. Then the BFO analysis came out. This was far more complex than the BTO analysis. It took time, It required corroboration by independent scientists. And there was likely a degree of circumspection in various quarters. None the less, the BFO analysis identified a likely area - not so far away from the area now thought to be most promising.
4. Then came an air search. Due to all the delays, it was already very late when this was started. Even if debris had been found, it would have been difficult to backtrack. However it was the best hope at the time, and so began a multinational air search that was complicated by the distance from land and poor weather. This was only called off when it was clear the delay meant that backtracking would be futile.
5. At some point, the search area moved a long way NE along the arc. It has never been made clear why this happened. People have speculated that a UK submarine detected something that could have been a pinger, but we will likely never know the explanation for this. Ships went to this new area and seemed to have immediate success finding the pinger. It turned out there was no pinger and the noise heard came from the ship. Yes that was all a bit of a screw up.
6. Hence back to the BFO data. The highest probability area was calculated on the basis of detailed calculations and utilising different models, and is fairly close to the earlier area. So they started to map the ocean floor (this area is practically unknown) in preparation for another search.
7. They have now incorporated information from an unanswered call to help refine the search area. Presumably this data pushes the search area a little further SW.
On top of all this has been significant political and diplomatic pressures. There was certainly an initial reluctance on the part of the Malaysians to tell all they knew. The Australian Prime Minister was under pressure, and jumped the gun based on satellite photos of debris.
Its not been perfect. Far from it. Things are always easy in retrospect.
In fairness, it has probably been about as good as could have reasonably been expected in the real world. This is especially true given this event was unprecedented, and given we have been using technology in novel ways.