LeDuc operated a ramjet at high subsonic speeds in the '50s. Nobody today would consider really operating one there - it’s got no real advantages.
You’ve already hit one of the biggest advantages of the ramjet/scramjet - no moving parts. In a turbojet keeping the compressors and turbines alive is one issue at high speeds - pressures and temperatures get quite high. Keeping rapidly rotating machinery at tight tolerances at high temperatures gets rough. In the ramjet you can largely separate the structural and high temperature resistant components of the engine. There are also fairly high losses through the compressors at high speeds. As a result of this (and other factors), at speeds above 2.5 times the speed of sound or so a ramjet has a higher specific impulse (is more fuel efficient) than a turbojet.
You are also ignoring the other alternative to ramjets - rockets. By using atmospheric oxygen ramjets get much better fuel economy (propellant economy?) than rockets. So perhaps if you are launching a missile from an already supersonic or high subsonic plane it makes more sense than a rocket if longer range interests you. Or if you are trying to extend the range of a munition fired from a gun.
There are two “combined cycle” engines that get played with a lot. Rocket based combined cycle, or RBCC, and turbine based combined cycle, or TBCC. They use rockets and turbojets respectively to reach ram speeds. Relatively lower speed apps (cruise missiles, etc) tend to be based on TBCC.
The RBCC typically has rockets integral to the flowpath of the engine (with or without the inlet initially being blocked off). The idea is you start flowing fuel and oxidizer to get moving. Once you are moving and injesting air you can run your rocket fuel rich to take advantage of atmospheric oxygen (this is an “ejector ramjet”). Once you are in comfortable ramjet territory speed wise, cut off the oxidizer and run as a ramjet. If you fancy a little more speed transition to scramjet mode at higher speeds (Mach 6 will do nicely). If you want to go to orbit just pop the rocket/oxidizer back on at some point between Mach 8 and Mach 25 and there you have it, a lovely little single stage to orbit spaceplane. You get to carry a lot less fuel but require significantly more structure than a pure rocket.
A TBCC may have two internal flowpaths - physically switching between the two. Depending on your application you might or might not turn the turbine off.