Why rotary engines are not used widely?

Hard to get them to meet new emission standards...its impossible for Wankel/rotary engines to meet emmissions standard due to a serious fundamental design flaw. That is, the piston crown and combustion chamber surface area ratio to the cylinder and combustion "chamber" volume. The dish in the middle of the rotor. Its like a very (very) short stroke conventional engine. This results in a very large dead space (typically referred to as squish area) when the piston is at top dead center (TDC). This squish area ejects a large portion of the air to be used for combustion, into a more compact chamber either in the cylinder head, or in the piston or rotor crown (as is the case with the wankel). While this "squished" air help generate turbulence for an effective and rapid burn at ignition, there is (in the wankel) a large portion left in the space between the rotor and cylinder perifery, which, while it eventually burns, it doesn't burn efficiently (completely) through the period of peak compression. Further, there is a zone around the rotor sides where there is more dead space above the rotor side seals and chamber that burns very late and poorly in the process. Further to all this...when the rotor is at TDC, there is a large...I mean "large" banana shaped area each side of the rotor "chamber", between the chamber & rotor tips with a massive surface area vs volume of air for combustion. This banana shaped volume creates a very long path for ignition and the surface area quenches a lot of the initial heat from the ignition and impairs the combustion reaction markedly. Having said all this, the wankel engine is a very mechnical efficient design, albeit with an inherant serious flaw goemetrically impossible to over come.