The difficulty of getting compliance even in the face of a scary new threat should give a good deal of indication of how hard it'd be.
And the speed with which it spreads in a population that has little immunity against the current strain should be a good indication of how little you'd save.
Eh, there may be a certain amount of truth to that, but personally I think it's one of the many fears that sci-fi has overplayed.
Part of the problem we have in our war against infectious diseases is that they mutate in endless variety. The cold you catch tomorrow is slightly different than the cold you had last week; the variety of the seasonal flu spreading this year is different than the variety of last year.
But these endless varieties are generated at a rate proportional to the available hosts. If we can successfully reduce the number of hosts available, we would also reduce the number varieties of colds and flu we have to contend with, and the rate at which new ones appear. Everyone not getting a little sick all the time might conceptually weaken our immune systems, but it would also weaken the diseases against we're fighting, and we would still have our other tools we use to fight them.
And the speed with which it spreads in a population that has little immunity against the current strain should be a good indication of how little you'd save.