First released JWST images are amazing. However, given the amount of image processing, false colours, cleanup etc. that must have gone into these images, why not also remove or reduce the diffraction spikes on bright stars ? Since these are purely artefacts of the telescope construction and have nothing to do with what is being imaged.
Simple answer: false-color does not in any way "photoshop" the original image information. The term "cleanup" doesn't mean anything. Quite probably multiple images were collected to reduce Poisson noise (both photon and sensor readout), but again that does nothing to manipulate the actual distribution of photons on the image plane.
While diffraction spikes can be removed given solid knowledge of the telescope's mechanical construction, no matter what you do there will be some loss of fidelity. (By way of comparison, you could look up methods for removing pure spherical defocus error in an image, for example)