You see, if power was distributed over many thousands of independent miners, all such lists would have thousads names
This statement is logically false.
I forgot the word 'evenly' before 'distributed'. (I used it elsewhere when saying that same condition.)
Is that why you did not understand the logic?
I did understand the so called logic, but it was false.
It is false because it assumes all such lists are showing power, but in fact they all show something else, generally pools. I've never seen a "mining power list," have you?
Even with a relatively small number of pools you can still have power distributed over many thousands (or even more) independent miners, because those miners are able to move their hash rate. No pool can be confident of maintaining a given share because hash power can shift and new pools can be created.
In fact this was not the case with ghash since much of their mining was their own equipment.