The thing is, though, one of the defining characteristics of a LASER is its spatial and temporal coherence. In other words, all the light waves/photons (I'm not going to get into quantum mechanics on this forum) have to travel in lockstep. That means, all the same size, energy, and color...all traveling in the same way; each precisely mirroring the motion of the photon in front of it, and behind it. There's no internal interference.
3 beams...red, green, and blue, will *never* all travel completely in lockstep. Even if you manage to get them perfectly combined, they will NOT be a single LASER beam, and the waves internal to the combined beam will interfere with each other. Even the output would not be white (though our eyes would probably perceive it as white) because there would be 3 discrete frequencies of light, and truly "white" light is spread across the entire spectrum.