I would support this 100%.
I would add that if there is an important reason for a change in your track or level then tell the controller that at the time. Even on CPDLC a free text DM could be added to a climb request. perhaps "DUE WX". If the controller knows that there is a potential reason for concern then the normal procedures can be short-circuited. In this case close to an FIR/UIR boundary instead of asking the next controller the controller could have immediately cleared the climb, then tell the downstream controller that an aircraft in the 'area of common interest' has been given a climb, apologize but the climb was allowed due weather, expect following aircraft to climb too. It happens all the time. Tell the controller about severe weather, it will affect how (s)he reacts to responses for deviation or level changes and sector transit plans may be eased out a little so there is space for you and following aircraft to make deviations.
This. In the end, the PIC is responsible for the aircraft and has the legal latitude to deviate from ATC instructions to the extent which, in the PIC's sole judgment, is necessary for the safety of the flight. Exercising that authority is still an issue in the West and I can imagine it being more of an issue in parts of the world where deference to authority is more strongly inculcated as part of the culture. Conversations here tend to discuss deference to authority in the context of CRM; what I'm suggesting is an issue between PIC's and ATC.
"Unable", "declaring an emergency", "PAN, PAN, PAN" should be encouraged in events where there is an issue with the possible safety of the aircraft. Better to deal with some paperwork and maybe a call to the chief pilot's office or a hearing after the fact than winding up in the morgue.
This also implies that there are cases where you may need to communicate first in order to aviate. Yes, this goes against the grain of conventional wisdom, but, once done, you have full latitude to aviate.
Bottom line: use your legal authority to the fullest extent to get your passengers (and yourself) safely on the ground and don't be reticent about it.