[FUNALA]

There are many complaints about the overpopulation of deer but most also abhor the most efficient method of control (trapping or drugging deer, and relocating them is extremely expensive [don't raise my taxes] requiring much manual labor).

And where are you going to take them? Nobody else wants them either because the same problem now exists over much of their range, so no other state/county/whatever is going to agree to have your problem dumped on their doorstep. As you note it's expensive and it's not very effective either, why are the deer in the suburbs eating somebody's garden anyway? Food. If you dump one out in an area that's already overpopulated and thus short on food within a few days it will be looking for someplace with more forage available. That population pressure is going to drive another deer right back where the one you just spent $10000 trapping and shipping out came from. The only thing that works at a reasonable cost is reducing the population by hunting them.