Agreed. I believe this actually happened in Civilisation III with resources like aluminium and uranium... another fine strategic element which could be added, I think.
As someone whose first ever modding experience with Civ was painstakingly removing that feature for every resource every game, let me explain to you why I (and hopefully I am not alone)
hated it:
It has nothing to do with the effect of resources on an empire as a whole - if a resource runs out, you go and find a new one and then you're back to where you were. It has to do with the effect on cities founded near the resource that goes away.
Cities are founded based on the terrain that is around them, i.e. next to a river, right amount of hills, forests, and plains, on or off the coast, etc. Resource bonuses are a critical part of that planning, and to have one spontaneously vanish with no warning and no way to fight it can completely devastate a star city. Having one of your cities suddenly just get worse can invalidate hours of gameplay investment.
Things that change your situation and force new strategies can be fun, and they have their place. They should be
obstacles, though, not permanent changes. An obstacle is characterized by the ability to overcome it and eventually return to where you were before. When a resource ran out in civ3, that was the equivalent (in city yields) of losing a entire citizen (or two, sometimes). Imagine if there was a random event that said "one of your citizens is now permanently unavailable for any purpose, but still requires food and affects you cities health and happiness".
The event where goblins dump waste on your land and the food yield is permanently reduced by one is a current example of this kind of effect, although it does give you a nature mana option. I don't think there is a single event in the entire game that I hate getting more than this one. Fortunately 19 out of 20 times it's happened on a mountain or outside a city radius.
Simplified, my point is this: don't put a goal in the game (resources in this case) that requires effort to acquire but can then be taken away entirely at random. Make it:
A - reversible, either time or a specific player action restores the loss.
B - preventable, through means that is readily available (goblin dumping frequently occurs long before having nature mana is possible.)
C - optional, tie the loss to something that is not a practical necessity.