A big selling point of the ramjet is its absence of moving parts (hence why it can be translated as "statojet" from other languages). However, an even bigger drawback is that a ramjet cannot produce static thrust, thus a ramjet-powered aircraft cannot take off by itself.
The problem is that by solving the no-static-thrust drawback, adding a turbojet negates the no-moving-parts selling point.
There are missiles that use solid fuel rockets to solve the problem, using the exhaust of the rocket to compress the air in the ramjet, which is sometimes referred as a ramrocket. However, there doesn't seem to be aircraft using this kind of engine, and missile engines have quite different constraints.
Is there an aircraft engine, working or theoretical, that works as a ramjet in cruise mode, can take off on its own power (without requiring ground installations or a detachable first stage/mothership), and doesn't have the many complicated moving parts of a turboramjet? What are its expected characteristics? If not, what are the showstoppers?
And why can't we simply inject some oxidiser (for example WFNA) to produce static thrust?