Ian W and Air Scotia :
ATC do precisely that.
Maybe in the USA where there is an old " CB avoidance" culture and ATFM ( Flow management) organised through a single command centre which has direct access to the US Air Force areas .
Europe is also equipped with an advanced centralized ATFM system , but does not have the same weather pattern as in the equator/tropics or continental US. and there are 40+ airforces around to deal with.
A totally different picture that what is going on the rest of the world unfortunately , and definitively in South East Asia , where each Sate has its own air force and where countries are suspicious of one another and do not cooperate.
ATC is there to separate aircraft from one another also aircraft from penetrating reserved or restricted areas, and to comply with restrictions and demands made by teh next sectors( control centres) .
There is no standard " Miles in trail " separation applied by all. They vary depending on location and surveillance capabilities. , it can be 5 NM . can be 100 Miles (15 minutes) . It can be 5 NM in one sector , and 10 minutes at the transfer point for the next sector in a different Control Centre no equipped with same capabilities. Once established controllers have to follow that.
But, once again , the pilot has the decision on weather avoidance, not ATC . The pilot(s) can see in real time what the actual weather is , ATC cannot. If a request for deviation ( laterally or vertical ) cannot be approved by ATC ( due e.g. restricted or dangerous areas penetration or simply other traffic ) the PIC can deviate on his own bu just declaring on the R/T , " unable, turning or climbing now ". This then becomes an emergency situation , and ATC will help clearing the way. The PIC is always ultimately responsible for the safety of his flight.
To come back to this Air Asia case, I have seen no indication so far that the Pilot of this flight did not jut do that, but he did not tell ATC, so for me I think there must be something else, or the initial request to deviate came much too late.