Not the OP, but evolution will often select for less energy expenditure as most animals are calorie constrained or at least during certain times of the year (c.f. animals that hibernate to survive low calorie availability).

It seems plausible to me that the immune system might be calorie intensive to be on full alert all the time. However, I suspect that having the immune system be more active will likely lead to other complications such as autoimmune disorders or even something as common as hayfever.