There's studies on "brain training" apps like Lumosity that tend to show that all you're improving at is the specific test, not the underlying mental capacity like working memory.

And a related anecdote: I once asked my psychologist to do an IQ test on me, mainly out of curiosity. She refused, basically giving the logic you did. We have no reason to believe your IQ is low, or even average, and if we did do a test, and at some future point we needed a test for actual diagnostic purposes(say if I had a stroke or something), it could taint the result.

So I'd say you're right on the money wrt the limited usefulness of doing these neuropsych tests repeatedly. Especially over short periods.