How to express in a diplomatic, but not too subtle, way that an old (and popular) notion should be dismissed in favor of a new (and better) one?

Solution 1:

supersede, as defined by Dictionary.com

to set aside or cause to be set aside as void, useless, or obsolete, usually in favor of something mentioned; make obsolete: They superseded the old statute with a new one.

Steven Weinberg (Nobel Prize winner in Physics, 1979) used supersede in this way in his book Lectures on Quantum Mechanics, page 21:

It was hopeless to use matrix mechanics to solve more complicated problems, like the hydrogen molecule, so wave mechanics largely superseded matrix mechanixs among the tools of theoretical physics.

The OP's sentence thus becomes:

In a way, what we have just remarked makes the notion of functoid à la Craig and Daniel superseded by punctoids.

I suggest rewriting the sentence to say:

In a way, what we have just remarked means that punctiods supersede the notion of functoids a la Craig and Daniel.

Footnote about the use of a la in a math article: See Using the Mathematics Literature.

Solution 2:

Consider "deprecated". See https://www.merriam-webster.com/words-at-play/deprecate, however.

According to this note, it's been used since the 1980s to imply obsolescence, although MW questions this use.

You can be more positive by noting that the punctoid is superior or better in a variety of ways (more flexible, less prone to error, whatever).

Thus:

The functoid should be deprecated in favor of the punctoid.

A milder approach is to say that the funtcoid approach should be replaced.