By "silly" NOx emission rules - I presume you mean silly in that they've enabled both the manufacturers to cheat - as in VW, and the consumer to cheat, as in the case of disabling EGR and/or re-mapping ECUs to improve performance and fuel economy.
Reducing NOx isn't a silly idea - except perhaps in a rural area where that pollution isn't a major issue.
The "Atkinson Cycle" petrol engine (so called - actually not a true atkinson cycle but achieves the efficiency benefits with less mechanical complexity) is very efficient but not great power : weight ratio. As used in Prius etc, low maximum engine power can be compensated for (somewhat) by boosting performance using the electric motors.
Mazda's extremely high compression petrol engines (as well as current direct "stratified" injection high compression or forced induction petrol engines) have an inherent problem that they produce very fine nano particulates. (Unlike indirect port or throttle-body fuel injection) The full long-term health impact of exposure to these is unknown, but these do go straight through the lungs into the bloodstream, there's growing evidence that they may be extremely harmful, IIRC to meet future Euro emission standards, direct injected petrol cars will require a DPF system like diesels.