MTOW is a hard limit regardless of other considerations and is tied up with the basic aircraft certification basis.
In general true, however for stuff like airway or landing fees the MTOW can be flexible again. We use around 8 to 10 different MTOWs and select the lowest usable for each flight. That MTOW is then the basis for all kind fees associated with that flight. The highest usable one is the certified one, which does not necessarily have to be the structural limit, some of our 738 have around 75t, others over 78t. Just a matter of certified max weight which can be changed whenever there is any need.