This is a remarkably deep question. In principle we want the two to be symmetrical. Sound field around the microphone becomes the sound field created by the speaker. The trouble is that idea breaks down almost instantly, and it just becomes worse as we go on. Indeed the trivial intuition about stereophonic reproduction breaks down almost instantly for the same reasons.
Moreover microphones don't even all work in the same way, condenser capsules register air pressure, ribbons air velocity, and yet we assemble the response of both into the same result and feed the result to loudspeakers.
There is a chicken and egg (not far off a circle of confusion as well) with microphones and speakers. It is hard to deconvolve the level ambience captured (or faked up) in a recording from the manner in which a loudspeaker interacts with the listening room, and thus how a loudspeaker is designed, especially with respect to directivity. Loudspeakers used for mixing are in a way designed and set up for use in a way that is both informed by the expected final listening environment, but during tracking the loudspeakers (often the same loudspeakers, but not always) are being used to directly monitor the result of a microphone's output.
Close mic'ing means a totally different recorded artefact to say an orchestra recorded with a Decca tree, ORTF, crossed pair etc. Yet in the end we send the result to the same speakers in our listening rooms and expect all to sound good, if not realistic. Loudspeakers are designed to work across the range of recording techniques, and those techniques are designed to work well feeding our current designs of loudspeakers. Yet Siegfried Linkwitz spent a lifetime working on an improved speaker/room system that he felt created a better in-room result from those same recordings.
I think it is fair to say that speakers are indeed designed for microphones, but the relationship is, as they say, complicated.
