That definitely sounds wrong - if you're leaving unburnt fuel in your exhaust, that is wasted fuel, you could burn it further and get more energy out of it - they seem exactly in line with eachother as goals. Do you have any source for that statement?

It's not that there is unburnt fuel in your exhaust - unburnt fuel, while a pollutant, is not the problem.

The issue is that higher temperature combustion, while more efficient, produces much more NOx. So you get more energy per unit fuel at higher temperatures, but you also get more pollutants. Lower temperatures (less oxygen) result in "cleaner" combustion (essentially, more CO2 and N2, less NO and NO2), but produce much less energy per unit fuel.

This is only true in some regions. The creation of Ozone in the troposphere is dependent on availability of NOx, and availablity of hydrocarbons. In the southeast US, forests produce large amounts of volatile hydrocarbons, so the system is NOx-limited. In California's Central Valley, excess NOx from nitrogen fertilizers makes ozone production hydrocarbon-limited (and also basic rain from the NH3). So from a pollution management standpoint, either could be important, but usually only one.

I had forgotten about the NOx at higher temperatures. But running lean is also more efficient and can result in incomplete combustion:

https://en.wikipedia.org/wiki/Lean-burn

There really is a lot at play, but I stand by the statement that "clean" and "efficient" are directly at odds with each other.

"directly at odds" is going too far.

For example, electronic fuel injection is cleaner and also much more efficient than using a carburetor.

Unless you build lighter, more aerodynamic, smaller cars with batteries, then you get both less emissions and greater fuel economy. Cheating is easier though.

And when you make the car lighter and smaller, you worsen passenger safety, and possibly increase costs (depending on what you're using to make the car lighter).

Lighter, smaller cars are actually safer.

An independent review of the impact of California's CARB emissions regulations found that if you totally ignored the health and climate change benefits, the regulations were still a net benefit just because they encouraged lighter cars, which lead to less death and injury on the roads.

Possibly you're thinking, but if my car was bigger than everyone elses, then I'd kill them, instead of them killing me. But unfortunately, everyone else is thinking the same thing. A classic case for regulation leading to improved outcomes for everyone.

There's lots of leeway to make trucks more aerodynamic. It's the biggest low hanging fruit.

This is fascinating and, like you say, counter-intuitive. Can you expand on this or provide some links?

As someone else pointed out, it's not "incomplete combustion" it's production of NOx which is a pollutant. Running really lean also results in a bit of incomplete combustion though.