Calculator asks you to rate it in the app store...

You're the preinstalled calculator!! You don't have to compete with other apps!!

The desperation for feedback is grating. You have a monopoly position, you know I cannot switch from this, why waste my time with this dialogue? Not like you take user opinions seriously anyway.

Just an act of asking for the opinion matters.

(Maybe not for all, but definitely for some)

https://en.wikipedia.org/wiki/Hawthorne_effect

That claims surveying workers improved their productivity at the job.

I don't think you can apply that to be interrupted with a popup while using a calculator.

There probably is a second order effect - designers who have heard this, are more likely to add survey/feedback form into an app. (Even if first order effect is not real)

Hey Calculator, how many R's are there in strawberry?