Rare question about interaction terms, main effects, and mean-centering - mix & match?

Question

This question is not about the longstanding discussion of 'to mean-center, or not mean-center' interaction terms, or what mean-centering the variables in an interaction gets you (or doesn't get you).

The question is if it is reasonable to have a model that includes an uncentered predictor serving to model a main effect (e.g. Education's effect on income), and an interaction term that is computed by multiplying a mean-centered version of that variable with another term (say, gender, to see if the education effect on income is conditional on gender), while leaving the 'standalone' education variable on its original scale.

For the sake of keeping the focus on this rare combination of an uncentered version of a variable with an interaction that is based on a centered version of the same variable in the same model, let's ignore the reasons for doing this (i.e. interpretability vs. collinearity).

Everything I can find about these issues seems to always assume that either all versions of the variables (as an individual variable/main effect, and as a part of the interaction/product term) are either centered or uncentered. Hence the labeling of this as a 'rare question' about mean-centering and interactions.

My instinct is that this (mixing and matching centered and uncentered) is problematic because, despite the linear similarities between the centered and uncentered versions, you end up with a model where one of the components of the interaction is technically absent. But this may also be just because I am not a fan of arguments - still common in a lot of places - that collinearity is the reason to mean-center.

What do people here think?