"if you don't give up all your privacy to mega corp then you deserve to be blacklisted by society"

Thank you, I was feeling like I was very far outside of this thread until your comment.

It's somewhat unclear to me what you have to lose here. You're going to their retail store that is littered with cameras as a feature they heavily advertise. You're returning a package with your name and address on it. If typing your password into the turnstile is the last straw, that just seems weird to me.

But even that wasn't required. OP did their return successfully.

The loss of privacy comes not from actions taken at the Amazon store, but from having the app installed on the phone 24/7, including when you’re not at the Amazon store.

A somewhat similar example would be using Facebook purely through its Tor onion address, while simultaneously blocking facebook.com on your home network. The point is not to keep Meta from having any information about you, but to limit Meta to information it can acquire from your direct interactions, as opposed to the piles of unrelated browsing history it normally acquires through IP address correlation and Like buttons.

OK, I'll bite: what could possibly be the issue with keeping an app installed?

If you quit it it's not running, and if you don't give it location permissions it's not tracking your location.

Is there something I'm missing?

The situation has gotten better over time as the OS manufacturers have locked down permissions and made background operations more visible. But many privacy leaks have been only recently fixed or remain unfixed—for instance, it was only in 2021 that Android removed the ability for apps to collect the full list of installed apps. And there have been some real stinkers in the past, like when Facebook used its app to modify people’s contacts lists to make @facebook.com email addresses the primary. Companies that make money from aggregating data will always be on the cutting edge of these techniques compared to ordinary people. The app that’s not installed leaks no data at all, and I don’t blame anyone for avoiding apps that aren’t absolutely necessary.

The whole point of the go stores was to do retail in a different way, where you had to conform to their way or it wouldn't work. Yes, it was limiting for people that didn't have a phone with them or account info. Do all of these people befuddled by the phone/app requirement for go stores struggle when they go to pick up something at an amazon locker? It's basically the same thing, you can't "talk to someone" to get your locker opened that is on the back wall of the drugstore.

You can access an Amazon locker with a barcode printed from the Amazon website, or even from your confirmation email. The app is not required.

good point - I forgot about that. I added my son's account once to access a locker for pickup too.

What's the problem with cash? Counting change make you feel like a dummy?