Does this change improve the resulting binary?

I hope so. - I propose to give the refactorings "Reduce scope of variable"
and "Extract a function" (and the corresponding consequences) another look.

I.e. does it make it smaller or faster?

It is generally possible that a specific code generation variant will also affect
the run time properties you mentioned.

Otherwise this change is useless churn - you're making the code more
complicated, longer and harder to read for practically no benefit.

I imagine that there other reasons you could eventually accept
for this use case, aren't there?

Regards,
Markus