Generally, one would obtain approval for a deviation. However, if the need becomes critical, ATC comms are poor, or one is in an uncongested area then it is, in my opinion, better to analyse the risk and deviate anyway if necessary. With modern TCAS systems the risk of conflicting with other traffic are greatly reduced.
I would add though, you wrote that very diplomatically..
it is not only better to deviate without clearance, it is an absolute "MUST", the rules of the air stipulate that a pilot in command, being responsible for all that is happening is "REQUIRED" to deviate from "rules of the air", in this case from obtaining a clearance, if the safety of flight requires immediate action..
so, out there, in the boonies, where the folks at receiving end of the HF may have gone out for lunch, maybe not even having my flight plan, because somebody forgot to add the AFTN address of their FIR, hell, I would not wait any second for some "deviation clearance" or some rerouting, I'd always deviate first, whichever direction I would deem fit, knowing that any potentially conflicting traffic , like me, also is equipped with TCAS II, and I would see any traffic problem on my TCAS either as a TA or ultimately as an RA..
I suspect however that some folks nowadays wait too long in such situations for "reclearances" and may by that fact alone end up in some very difficult situations..
that should be addressed in training nowadays..