We have been running the old D&D adventure Isle of Dread when we tested the alpha rule and I can't say that we have run into any problem with WP spending and gathering. When you push yourself, you hurt yourself and since you can't heal unless you rest (and that takes 6 hours). In a system where your attributes are between 1-6 and the attributes also contributes a lot to the skill rolls, it isn't that fun to damage yourself just to get a WP or two.
The easiest way to get WP is of course through combat, because you roll a lot, but the push combat roles are very dangerous because you will be damaging Strength and Agility (for the most part) and that will decrease Strength and Agility skill rolls and also take you one step closer to become broken. You do push in combat from time to time. When it is tactically good to do so will come naturally.
The wilderness and camping events is another big bit of the game but since failure will have serious consequences (for the entire group), pushing such rolls is double edged sword. You get WP and perhaps you succeed but you usually make one roll to guide the group and one to build camp. So if you get damaged when guiding the group your build camp roll or hunt roll will be rolled with fewer dice. A failed camp usually means no good rest and no good rest mean no healing and the next day will be even tougher since you start already damaged.
In my group I noticed that if the survival skill rolls starts to fail, the entire group is in serious trouble.
So it is easy to say that the players will push just to get WP but this is a tough game to survive and the players will probably not be doing that for long. Then of course that can be me that is a harsh GM. But in my game, the players have pushed their rolls when they needed it and they have earned and spent WP quite well. They haven't push a skill roll that hasn't also been necessary.
This game, much more than MYZ (or perhaps FLs other games), it is much more important to let the players design a good group that have distinctive roles so everybody becomes useful. It will probably be a good idea to let the players really discuss the group dynamic.
“I’d say thistles, but nobody listens to me, anyway.” - Eeyore