Caveat: I'm not an evolutionary biologist.
It probably has something to do with the fact that non-aquatic animals breathe through our faces, whereas most aquatic animals have gills. My (cursory) reading on mouthbrooders indicates that most either do not feed while brooding or feed very little. This indicates to me that the mouth is almost or completely blocked by the brood. Even if a non-aquatic animal could survive a brooding period without eating or drinking water, we can't live without air. Anything that could put pressure on or potentially block the throat is dangerous to us.
So, if you want non-aquatic mouthbrooders, you might have to give them gills. It would be difficult to justify this from an evolutionary standpoint, however, since we spend most of our lives not brooding. Any orifice in the body is an opportunity for infection, which is why evolution favors fewer rather than more; look at how many species have cloaca instead of separate orifices for urine, solid waste, and reproduction. Mammals are basically the exception here, all other vertebrates favor cloaca. So, to develop a separate orifice (or two) for breathing during the few months out of their whole lives when an animal might be brooding, rather than using the perfectly serviceable orifice* in our faces, would require some strange kind of evolutionary pressure that made either gills or mouthbrooding absolutely essential. Aquatic animals, of course, developed gills because they have to filter oxygen out of the water. Perhaps there is something in the atmosphere on your world that the non-aquatic animals need to filter. This might give justification to the development of gills and, in turn, the feasibility of mouthbrooding.
*I am here referring to the throat. Technically we breathe through three orifices; the mouth and two nostrils, but since they all connect to the throat, I am considering them as a unit.