Are you not in the US? Maybe it's different elsewhere, but my nexus 5x died a little while ago, and I only had the default warranty, not the extra protection, and it was insanely easy to get a replacement.
I filled out the form[1] (saying I had already tried the usual android-saving moves), got a call back in two minutes as promised by that form, the customer service person accepted I had already tried things and didn't ask me to do anything else, then I immediately got the email with the link to get a new phone shipped to me. Was probably less than 15 minutes of my time.
(you also seem to be talking about something else than the OP. If your phone died in two weeks that's definitely under the warranty, regardless of if you purchased extra protection).
[1] linked here: https://support.google.com/store/answer/6301527?hl=en