Ironically, I think there is a link there. I am more likely to relax my disbelief if things look real. Once I have immersed myself into a situation I believe ( because it seems real ), I am less likely to pay attention to things like shot count.
It is the same as having heros that struggle with situations early on and then later are effortlessly capable of so much more. I already believed them so now they can take advantage of that.