It'd be especially useful if they could run on regular jet fuel, then turboprops/jets and pistons could use the same fuel infra.
Diamond Aircraft have had success selling planes with diesel engines recently, and even started a subsidiary company to manufacture them: https://en.wikipedia.org/wiki/Austro_Engine
In the early days of aviation (like 1930's or such) there was some effort to introduce diesels for long-range aircraft, the idea being that the heavier powerplant would be offset by the lower required fuel load due to better fuel economy. But they weren't successful.
More recently there has been something of a renewed interest in aviation diesel engines, the motivation being they can run on Jet A-1 in addition to diesel fuel. Jet A-1 is what jet (and turboprop) aircraft use, and is available at basically every airport worldwide, is much cheaper than avgas, and no risk of being phased out like the leaded avgas being discussed in this article.