Not to be rude, but this is my conclusion based on what you wrote.
You cracked the screen on your brand new phone, and so immediatly bought an otterbox defender case to put it in so that you could illicit sympathy from the people here.
How do I come to that conclusion? You wrote:
Typically I am not a fan of phone cases. They're clunky, annoying and in my opinion detract from the overall appearance and usability of the device.
As a person who had a note 2 in an otterbox, I feel the same way, this case doubled the thickness and weight of the phone, and I never even dropped it once, so I do not use cases any more other than minimal ones, such as the Silicone case that my note 20 ultra is currently in.
So to me, someone who hates cases, would NOT buy the biggest, bulkiest one before even powering on the phone.
Also, your picture of you phone shows a disregard for its safety, as what it is sitting on is far from level. The crack itself, should not even hamper it's functionality as it does not go over any lenses, so not even sure why it is an issue, other than asthetics.
As for the 100's of posts about this happening, I have not seen 1, not for the Note20 Ultra, which uses a different glass than the S20 ultra uses.
uBreakiFix is an authorized Samsung repair center. They are a place where you drop off your phone, and then either wait in their lobby, or come back an hour or two later and pick up your repaired phone. Two hours without your phone is WAAAY better than upwards of two weeks!