Perhaps they do these days, but back in the 1908-1914 time frame a propeller wasn't nearly enough weight to be as effective a flywheel as they needed.
Mixture control on the early radials (especially the Monosoupape) was horrible. Throttling the engine was basically impossible, and the valve timing was rather suboptimal as well. But they had good power-to-weight for the time--which made them among the best aero engines just then.
They were able to make incremental improvements to the basic rotary, which improved things like carburetion and valve timing, but other layouts improved even faster. It is likely that improved carburetors and ignitions resulted in engines that didn't need an immense flywheel, so the major advantage of the rotary was gone.
Plain radials could separate out the intake air from the crankcase air, which only helped with the power and mixture. And the inline (or vee) water-cooled engines had much less frontal area, making it easier to streamline the aircraft--plus they were able to extract similar power from rather less displacement. Though the radials could be (and were!) built to massive sizes (3000+ cubic inches!) for massive power, and were much more damage-tolerant than the water-cooled engines.
-soD
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