The question of how to handle metadata routing in fit_transform has come up a few times and we don't have a clear solution to it yet. This is the latest conversation: https://github.com/scikit-learn/scikit-learn/pull/22083/files#r811448325

A nice summery made by @lorentzenchr is:

1. Handle fit_transform as separate method with its own set_fit_transform_requests.
2. Merge the requests of fit and transform (error if inconsistent)
3. Distinguish between fit_transform that only calls .fit(X).transform(X) and the rest (where it does something meaningful).

Option 1 is the easiest to implement, but it gets confusing when users put transformers in a pipeline. The user wouldn't necessarily know which meta-estimator does fit().transform() and which meta-estimator would do .fit_transform().

Option 2 is doable by adding machinery in MetadataRequest and MetadataRouter objects. We can have a common test which makes sure fit_transform always accepts fit_requests | transform_requests.

Option 3 requires change in the base.py and probably leads to much more discussions than the other 2 options.

also cc @jnothman @agramfort