Each of those flights should have an alternate and be prepared (have enough fuel) to divert. If there is a fuel emergency then self-announcing is likely appropriate as the plane is coming down anyway, but that is multiple things going wrong.

A big part of it is what category of airport it is, and plane. General aviation almost always goes to self-announce (which includes some business jets perhaps, they often land at untowered airports) but not category 135 air travel or whatever it is.