@refirendum
While the engine-out NOx emissions of a properly done are fairly low, they are not nearly low-enough to pass US, Europe, or Asia NOx standards. The only reliable and robust way to meet current and future NOx standards is with a 3-way catalyst, because a TWC is better than 99% efficient at reducing NOx. A Three Way Catalyst will not work with any non-stoichiometric engine (like SPCC or Diesel). Not meeting NOx standards is what nearly sunk VW with Diesel-gate. This is the basic reason why Diesel engines are going away for pass-cars and why no one is likely to ever introduce another lean-burn gasoline engine to production. It is possible to meet all of the emissions standards with a lean-burn engine, but it is very expensive (at least an extra $1000 in NOx reduction aftertreatment) and the solution is not very robust and durability is un-proven. The engine-out NOx emissions of the best Diesel or HCCI engines are not even close to being low enough to meet US or Europe standards.
Today, engine-out emissions are not important as long as the engine can run stoichiometric, and now most new engines even run Stoich at full-load.
The SkyActive-X engine has too many expensive features: Diesel-like fuel system, Supercharger (required for the combustion system), Cylinder pressure-sensor system (also requires a powerful ECU), and lean NOx aftertreatment (will use Ad-blue (Urea injection)). The SC is more expensive than a turbo, and pressure sensor system is not used by anyone in production yet.
The Skyactive-X is not a true Atkinson-cycle, it is a Miller-cycle engine which is in production by many companies. This is an example of a true Atkinson engine: https://www.youtube.com/watch?v=8HI_upMJ-q8
Many companies call their Miller cycle engines “Atkinson cycle
True Atkinson, Variable Compression Ratio, Divided Exhaust Turbocharging are some examples of promising future engine tech.