Looks like I'm one of the few lucky ones to actually receive my metal card yesterday (Friday 3/31). I called Amex at 9:23 AM Eastern on Thursday, and the rep sent FedEx First Overnight (AM delivery next day) without me even asking. Sure enough, the card came to my office at 8:30 Friday morning. First use was for a $3.00 coffee cake at the Capital One Cafe--yes, ironic as it is that they accept Amex.
One potential disappointment is that the new card has a different 4-digit security code and 03/2022 expiration date. The Amex phone CSR assured me the expiration date and security code would be the same on the metal card as they were on the plastic card. I have about 20 monthly recurring charges of various sorts that go to my Platinum card, so it'd be a hassle to change the card info on every single one.