I think abilities like Price of Progress are a really neat concept, you just have to be careful how you manage them- if the models that end up having it have a lot of NEAT triggers but not necessarily devastatingly POWERFUL ones, it becomes a cool "toolbox you can access at a cost when you need it, but won't always use," which encourages player choice.
The DANGER with an ability like that is either making the triggers necessary for the model to be worthwhile (in which case unless they're really powerful, it'll just end up killing itself trying to be useful) or making them so powerful that the 1 damage is trivial.
Done properly, though, it turns health into a resource- more resources for players to manipulate is always a good thing from a design perspective.