I don't know about Discover, but I totally agree with you on the ease of the claims process. I've made numerous claims under the extended return protection, the accidental damage/loss coverage, and the Extended Warranty benefit of my American Express Blue Cash Everyday, and it's been super easy each time. Every time they just asked for a receipt of the purchase and then gave me a statement credit except one - for an Onkyo receiver they wanted a repair estimate, I contacted Onkyo to get one and Onkyo agreed to service the receiver for free (apparently a common out of warranty failure that they were addressing).
I'm curious to see how Citi compares in the extended warranty department as their policy on the length of extensions (24 months on products with a year or more mfgr warranty vs. 12 on Amex). Bought some stuff on my Citi Double Cash but haven't had to invoke the Extended warranty claim yet. Did just invoke price protection (easy and quick) and have an ongoing claim for extended return window (dashcam that had quality issues that were not readily apparent at time of purchase and return window is gone).