If the jet hadn't come along, it's likely that prop development would have advanced to wankel rotary engines. Jets offered high performance and fuel flexibility that props couldn't match for military, especially when coupled with turboprops.
General aviation never really commanded the type of money needed to fund concentrated development the way the military could, that's why the Cessnas and Pipers and whatnot all use basically late 1930s/early 1940s technology for their engines.