I'd like to suggest adding an option to choose if a pre-comp inherits the label colour from the parent comp it was created in. This could live as a checkbox in the pre-compose modal, or if that wants to remain as uncluttered as possible it could be an option in Preferences > Labels.
The use case for me is project organisation - I tend to use one label colour for top-level shots, then colour-code pre-comps as needed. It adds a layer of additional management to go through and change the pre-comps so they don't have the same label as the top-level comps.