Plenty of ways to get that data without invasive tracking like GA.

I hate to be the one to break this to you but GA usually isn't as invasive as you seem to think. It's mainly tracking things like time on a page, links clicked, bounce rates, etc.

It's not deep scanning your hard drive to try and figure out your SSN or medical history like some people think.

Is the invasive part that the data is going to GA or that the failure-to-close-sale is explicitly being logged at all?

abandoned carts are pretty commonly stored in a database so a followup email can be fired off later in the way. You don't need GA for this.

Sure, you don't need GA for that. In the same way that you don't need AWS, you could just deploy to on-premises servers.

But people pick AWS because it offers a lot more than just a storage bucket. Same with Google Analytics. It offers a ton of ecommerce analytics including custom tags that can be set by the shop owner. TeeSpring is probably not a full-service Ecomm platform like Magento. It's likely that they are piggybacking on GA's built in Ecomm tracking and reporting capabilities, instead of reinventing the wheel by doing it themselves.

FYI, Ublock Origin also blocks links to "sponsored results" shown on Amazon search.

I hate when they do that. Obviously if I've abandoned the cart I had a reason for it, most likely the shipping fee is too high. If you haven't changed it don't spam me.