If you do something that causes air in one place to get 1 ppm dirtier and air in another place to get 1 ppm cleaner, and the populations are the same, the net impact on health cancels out.
But in general I agree that you should be able to look at tradeoffs of a set of actions and allow of the possibility that some negatives are offset by positives.
Not exactly. The other place might have people die from poverty, illnesses and godknowswhat much earlier so the effect of pollution shifting doesn't manifest itself or even gets masked off by rising life expectancies in general - that's the dirty secret behind the move of dirty and toxic productions to Asia.
The average ppm cancel out but the outcomes don't, because you have more sick people: Let's say 12 ppm is the maximum safe ratio for some pollution [edit: assuming it is a pollutant that has local impact, not like CO2 which has global impact]:
1) If place A has 10 ppm and place B has 10 ppm, then nobody is sick
2) If place A has 15 ppm and place B has 5 ppm, then people in place A are sick
Public policy generally doesn't work well with averages and similar analyses, because outcomes are usually discrete for each individual; it's not a stew where you can mix outcomes together and get something good.
As another example, if the economy results in one person making $1 billion and 999,999 making nothing, the average is $1 million per person - but what does that mean? 999,999 people are still in dire poverty. (It does have some significance, for things society does collectively - fund police and fire, and even help for poor people.)
It's actually slightly sub-linear, meaning that an increase for one group and an equal decrease for another group produces slightly less total mortality. See https://pmc.ncbi.nlm.nih.gov/articles/PMC9109601/#gh2329-bib... for some numerically fitted curves (search for GEMM).