dalter, what you said makes 100% sense. Hypothetically:
Team A gets 45 shots off, running slow down.
Team A gets 60 shots off, running average tempo.
Team A gets 75 shots off, running uptempo.
You said players get more tired with a higher # of possessions. But keep in mind, the other team also has to get the same number of possessions, despite what tempo they're playing.
So if Team A is running uptempo, they get 75 shots off, then assuming everything is equal Team B also has to get 75 shots off. But according to what you're saying Team A is getting more tired than Team B, because they are running uptempo.