errr if you are talking about the piegons then the reason is simple there are no piegon keepers in those areas to let them out in the late afternoons. Its not a hobby that west ammanis are known for.
the Arabic term for them is Kashisheen Hamam
I hope that's the only reason Salma :-)
Maybe they just choose to fly over the good old towns of Amman.
Interesting observation Leerna. I personally think that we don't have a spot to see over west amman since its up high so we don't get to see these flocks.