I’d avoid unique IDs, as then you need to track the ID in some way. I suggested local_{system_name}, as it avoided the need for creating more configuration files/options around (reducing bugs and the level of setup required to start using local wheels). It also resulted in a single additional tag (per platform), rather than many.
A custom platform (or platforms, as Archspec: a library for labeling optimized binaries could be useful in order to specify levels of features used) would be much more complex, as there’s choices about how to configure what platforms can be used, and an ordering of preferred platforms.
Local wheels seem to me to solve the quick override of a broken wheel (and quickly replaced when there’s an issue e.g. an ABI bump in a dependant happens), whereas custom platforms would solve the build a coherent and consistent platform for non-PyPI distribution (and could be used as a testing ground for new tags becoming available on PyPI, such as a musl/alpine tag). I’d suggest local wheels would have a higher priority than custom wheels (as local wheels are more specific than a custom platform wheel), but I’m happy to be convinced otherwise.