We all know that Bitcoin was designed decentralized in order for a powerful entity would not be able to control Bitcoin as a whole. Thank Satoshi for that. However, since Bitcoin has become very hot in the eyes of the public as well as governments around the globe, is it possible that they, the government, will be able to regulate Bitcoin? Let us say that an international body or a union of governments across the globe decided to takeover all Bitcoin mining facilities especially the ones that functions in full node. If that happens, can we consider Bitcoin as centralized and it is now regulated by the government?
There are two forms of governmental regulation that can be applied to Bitcoin.
(1) Are regulations applied to the on/off ramps of licensed monetary exchanges.
(2) Are regulations applied directly to and within the Bitcoin protocol.
The simple answer is that if governments throughout the world collectively took
control of all bitcoin mining facilities it would allow for "(2) regulations applied
directly within the Bitcoin protocol". In this event, that Bitcoin experiment would
fail since it was not able to resist this governmental attack type (Satoshi's original
decentralized mining theory was thought to minimize this type of attack vector).
If your scenario did occur, it no longer matters if Bitcoin is then "centralized" since
the proper viewpoint is that Bitcoin has been "infiltrated and neutered". It then
becomes an arm of those world governments, and if allowed to live, begins to be
used as a means to oppress the people.
Either way, it is not a total failure since with how Bitcoin actually functions, if
your scenario did occur, the Bitcoin community could emergency hardfork and
change the PoW/difficultly to bring back home mining, leaving behind those
attacking entities and their new infrastructure, and we would continue on without
them. It is a nuisance and would hurt Bitcoin/bitcoin temporarily, but Bitcoin in
this way would never be fully captured.
The real problem is not governments attacking Bitcoin as you described, what the
real problem is certain governments already controlling certain mining facilities in
the world and attempting to convince you to willingly want to go in their direction.
If that occurs, even the emergency hardfork mechanism is worthless since the
masses would be so ignorant at that point, they would desire slavery more than
freedom.