Deer ticks are not the only kind of ticks.
I suppose one way of fighting it analogously might be to reduce populations of sheep and cattle, but that seems likely to run into opposition.
Roe deer often carry all tick stages (larvae, nymphs and adults).
We are omnivores. We need vegetables AND meat to be healthy. I think what you meant to say is it's another way our overpopulation is biting us back. If we didn't have so many people we could still have normal herd sizes.
(Granted, it's likely the prevalence of said food that led to overpopulation... oh nevermind.)
My guess is some mixture of affluence (can afford to import meat from faraway factory farms), the factory-ization itself (meat is a cheap-ish commodity), and decline in cooking skills and time available to use them (most good vegetable-heavy dishes take more time and skill to cook than a hamburger does).
And I won't argue that we eat more meat than our bodies need. But then again, we eat more EVERYTHING than our bodies need. Most of that is likely due to our survival instinct that makes high calorie food taste appealing- protein, fats, and sugars.