You are correct that a horn is a mechanical transformer that increases impedance at the surface of the diaphragm. This increases efficiency, lower freq extension, and dispersion control. A shallow waveguide like you are planning can also help to improve physical time alignment on the Z axis, if you incorporate this aspect in your design. The waveguiding effect of a horn can reduce beaming into higher frequencies which increases the size of the sweetspot where stereo imaging can be perceived. However the shape of the horn affects tone due to internal reflections causing amplitude and phase distortions. Very few horn/waveguide designs are free of these tonal aberrations ime. See Earl Geddes for mo info on this. A DIY waveguide cut with roundover bit will have some of these effects but you won’t know if it is tolerable until you try it.
The total FR of the speaker and room response together is called “power response” and is more like what we really hear because we listen inside a room and we hear the reflections. Speakers with flattish power responses are said to sound better than speakers with flat on axis FR but otherwse poor power response. This is because the off axis radiation lights up the reflective surfaces which then color the direct sound. When direct and reflected sound are both relatively flat they add together to a relatively flat perceived FR by the listener. All listening positions tend to benefit from good power response. Thisnis why Harmon group speaker brands all tend to use waveguides or horns, because the waveguide controls how the HF is dispersed into the room. Their chief scientist Floyd Toole and team determined over many years of listening experiments that flat power response was preferred over speakers with only flat on-axis FR. This has become somewhat of a moral obligation in some speaker design circles. IME it can sound better and it can sound worse. In a well damped room its less important but few rooms are well damped. It isnt the only important parameter but worth considering. I personally prefer the sound of unloaded tweeters to horn/waveguides. ymmv