I'd like to request an input be added to multiple categories.

Use case: A production with 50+ inputs has a category for camera inputs, one for graphics, one for NDI sources, etc. But once in production, I want the 5-7 of the most-used inputs to be in a category of its own: My 4 main cameras, one NDI feed, and two of our primary graphics.

Right now, I can only select one category, but adding inputs to more than one category would improve organization and production workflows.

+1
but instead of categories an input should have a tag or more tags. Then the categories can be associated with these tags.

With this you can even organise a show in categories like "panel discussion", "lectern", "audience", "remote", "jury".... and just tag the inputs with the area you need them.

I've often thought this would be handy, but, at the same time, have been at a loss to explain how it could be implemented.

Right now, the cog changes color to reflect the category the input is assigned to.

With this new implementation, what would the cog do?