You can also stick a propeller on a turbojet to increase efficiency without the need for extra ducting though at a cost of cabin noise. That saves weight, but copying this design is a net gain at high speeds.
First, the various claims made by Stipa that jet engines were inspired by this aircraft are not credible. He even thought the V1 missile (pulsejet-powered) was derived from his concept.
"Stipa later claimed the Germans stole his patented ideas when they developed their V-1 flying bomb, although the pulsejet engine actually bears little relationship to his intubed propeller."
"Luigi Stipa died in 1992, embittered at not being recognized as the true inventor of the jet engine."
So it's a sad story for Stipa, but his indignation doesn't mean anyone stole ideas from him.
Secondly, the turbojet and turboprop were first patented in 1930 (Whittle) and 1929 (Jendrassik). These patents predate the Stipa-Caproni, which doesn't involve the Brayton cycle (obviously) so isn't really in the running for first jet propulsion. Now, you might argue that the ducted fan is a "jet" technology, but the absence of turbomachinery makes Stipa's invention very distant from either turbojet or turboprop.
Thirdly, you seem to be misreading the diagram comparing turbojet, turbofan and turboprop. It is the turboprop (not the turbojet, as you seem to imply) that is more efficient than the turbofan up to Mach 0.75. The propfan is exotic, anachronistic as far as the Stipa discussion goes, and is best thought of a high speed development of the turboprop. Early turboprops were prevented from developing into propfans by technological constraints back then.
Finally, when you "stick a propeller on a turbojet", making a turboprop or propfan, you largely give up jet propulsion. The exhaust of the turbine produces only a small amount of residual thrust. The Stipa-Caproni, being piston-engined, didn't have exhaust thrust.
Stipa wasn't working with the Brayton cycle or with turbomachinery. His claims that the idea for early jet engines (even the V1!?) were stolen from him seem really unlikely to have merit. On the contrary, the turbofan principle is suggested by the formula for propulsive efficiency of a turbojet. It's not a configuration, like the Stipa-Caproni, but a theoretical insight about jet engines that could be taken advantage of by adding a bypass. I don't see anyone claiming that Stipa saw this. A turbojet with a fan and bypass is not a copy of Stipa's annular duct. It is a lot more complex, and the devil is in the details.
The fact that Stipa went to his grave convinced that he deserved the credit for the jet engine is regrettable, but it would be a big surprise if he was vindicated. We all know people like him.
“The popularity of turbojets and turbofans curtailed research in propellers, but by the 1960s, interest increased when studies showed that an exposed propeller driven by a gas turbine could power an airliner flying at a speed of Mach 0.7–0.8 and at an altitude of 35,000 feet (11,000 metres). The term propfan was created during this period.[7]”
The sweet spot for propfans is therefore below about Mach 0.75 which is matches up with my reading of the graph.
The Stipa is a ducted fan, but the resemblance to a turbofan is superficial.
https://en.wikipedia.org/wiki/Turbofan#Principles