If you enter into a sales contract selling some gadget, then you are legally required to deliver that gadget, which also means you are required to deliver it without defects (unless those were agreed upon in the contract as properties of the gadget to be sold). If you happen to so far only have delivered a defective gadget, you haven't fulfilled your contractual obligations. You cannot refuse to fulfill that contractual obligation just because the buyer refuses to agree to additional terms that you ask them to accept.

Details obviously depend on the jurisdiction, but the basic principle probably applies just about anywhere.

> because they'd be required to collect and process personal information digitally, and they would be likely advised to not do so without defining the terms under which that information would be used.

That's absurd. First, they should only collect the information they need to provide a replacement product. Second, they should only use that information to provide a replacement product. That would be the right thing to do, regardless of how anti-consumer the laws in whatever countries are.

> The checkout process requires consent to their terms.

You can't arbitrarily weaken people's rights via terms in most civilized countries. So if that was the only way to get a replacement, I don't think it'd be too difficult to make a case that the terms are null and void. Certainly in Germany, additional terms such as EULAs are invalid if presented after the purchase.

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However, while the store might have been the most convenient way to get a replacement, I don't know if it was the only way. If they made it clear in the email that there were other ways to get a replacement, well then it's still a shitty move by marketing and ethically questionable, but probably legally okay.