Both things - that the number of patents measures innovation, and that they serve to stifle it, can be true at the same time. Under a fixed patent regime, the more innovation there is, the more individual patents are necessary to stifle it. Of course, if we allow the patent regime to vary, then if it changes to make patents easier to acquire then that means less innovation.
However, it's true that this property - of being a valid measure, but interventions to change it having the opposite effect on the inferred variable - is a very unfortunate one in a metric.
However, it's true that this property - of being a valid measure, but interventions to change it having the opposite effect on the inferred variable - is a very unfortunate one in a metric.