You have it wrong.
The colour camera has small red green and blue filters over individual photosites (pixels) and software then uses the individual pixel values to in a sense "decode" a colour image. Putting the camera in monochrome mode simply desaturates the already filtered colour image. If you then applied a red filter, only the red filtered pixels of the sensor would get any light, same for green and blue. Therefore, you would end up with the same overall image fidelity with 3 times the required exposure time, 10 times the amount of processing time and likely not as clean an overall result.
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