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.

An always full alert immune system won't have any lee way to address any onset of an infection, and also considering that pathogens also evolve to by pass the increased alertness, this will probably be catastrophic for the species.

That is unless of course like bats, this was the result of evolution and natural selection. But bolting on like this vaccine do it, yea, going to be pretty bad.