It's all a matter of time, which determines priority and pressure. The sick villagers are going to die. The mine isn't going anywhere, at least not as soon as the villagers.
And the people who would be helped by clearing the mine are going to stay poor - and probably edge-of-subsistence starving, since you favour a wasted world - right up until you clear the mines, after which their lives will begin improving. In either situation, you will do more good, to more people, if you act now rather than later. The time pressure is just as present in either situation.
To say that, if a person's act can improve matters, they are not causing a worse result by choosing to act later rather than immediately is to be wilfully disingenuous. So long as there is anything the characters can do to help people, there is an utterly real time pressure.
I agree. There are levels of infestations, and just general obstacles to player freedom in world design, and players will have different tolerance levels.
"Obstacles to player freedom" is, at least, a better term than "railroad". It's not accurate IMO, but at least it's not a misappropriated term that has an entirely different meaning.
The presence of scenery, creatures and people for players to interact with does not constitute obstacles to player freedom - though they may indeed be obstacles for the
characters. Instead, they constitute opportunities for player interaction with the gameworld - something that is essential if any actual game is to take place.
A good DM is aware of that too and takes it into consideration. Ideally he builds the world for his players and their characters with their desires in mind.
But in that case, why is the presence of the sick villager such an imposition and the presence of an infested mine not so? They're both built with the players' and characters' desires in mind, and they can both be acted upon or not as the players desire.
Whether the players' inaction will cause the world to become worse, or simply fail to make it better, is irrelevant to these choices on a player level. Those are purely character-level motivations, and it is dependent upon the characters, not the players, whether either or both situations will result in any feeling of time-pressure.