The first reason for looking south is because India and China and others would have seen that plane on radar once it headed over land and all of them say that it did not show up on radar.
The second reason is that ACARS would ping if the landing gear went down and there was no ACARS ping for that. So the plane either crashed in Kazakistan or took the southern arc and ditched in the waters.
The third reason is that the last engine ping at 8:11 puts it within the perview of US radar stations in Afghanistan and those stations saw nothing.
Thus by process of elimination they are looking south.
The key moments in the flight would be between 2:11 and 4:11.
Note that from 3:11 to 4:11 the plane flew along the same arc.
Do you seriously think any country is going to say anything about their capabilities and whether or not equipment was turned on or off?
I believe the ACARS like anything that is made can be defeated, by loss of power if nothing else.
Those arcs you see are based entirely on assumptions of contiuous flight in one direction. The aircraft could have flown in circles and crashed anywhere along any part of the arcs. There is nothing in particular about the terminal end of the southern arc other than 2 pieces of debris which do not fit with the facts.