A really really good reason to fill up straight after a flight is because it enables a quick departure later.
Once one is airborne, one has to land anyway (sounds stupid I know). Whereas a departure depends on all sorts of stuff, starting with the weather and, in many places abroad, involving the filling in of a pile of forms. The last thing one wants to do is mess about with all that and then not go because they can't find the avgas bowser or nobody can (or wants to) speak English.
In the same vein, all large airports want to get the occupants off airside really quick. You land and usually within minutes a van or bus turns up to get you out of there. This is a brilliant time to fill up. Just politely refuse to leave the aircraft until you have fuel. It's amazing how quickly they "find" the fuel then
