Refer to the laws of thermodynamics...
The amazing thing about polluting electricity generation is that it's more efficient than the polluting thermomechanical energy produced in your car by burning gasoline. Combined cycle turbines can be nearly 60% efficient, if memory serves... yes, that's 60% efficient still burning fossil fuel in some cases (though it's not that bad a deal if it's natural gas, at least in terms of particulates and other combustion byproducts)... however, that 60%+ thermal efficiency could also come from nuclear, which, if people were willing to trust something more complicated than burning things, would be as near zero pollution as you could hope to get (until fusion comes along in a few decades/centuries, anyhow). Or wind, or solar, or hydro, all of which have life cycle environmental cost, but don't necessarily involve burning lots of decomposed dinosaurs.
There is, oddly enough, still and upside even if it is polluting coal... think about the smog issues of LA, Beijing, and many other large cities. A good portion (the majority?) of urban smog comes from hydrocarbon fuel burned in the relatively inefficient (20-30%) internal combustion engines in cars, trucks, buses, non-electrified light rail, etc. From a health standpoint, moving that pollution load to isolated point sources to disperse over wide areas is probably far better than the low air quality common in cities. In short, you are correct, there is no such thing as a free lunch... but there are less expensive, and sometimes nearly free lunches, and also lunches paid for by other people which may be applicable to this conversation.