Chiming in here since OP is referencing my Reddit post. Indeed, Apple Support has repeatedly told me to wait for a future macOS update to resolve this issue.
A little background: Over a month ago, my M1 MBP 16" wound't turn on, so I brought it into an Apple Store for repair. They replaced the TouchID and logic board, and I used a fresh install of macOS without restoring from backup (some older posts suggest TimeMachine backup restores can also cause Wallet problems, this should not be the case here). Ever since, I have been unable to add any cards to the Wallet of my 16” MBP (they are immediately rendered as “Removed by Issuer”). Two tidbits I've found while troubleshooting is that a) the Previous Cards selection pane is not updated with the current list of cards on my iCloud account, b) the card verification page that usually shows up is skipped entirely.
I tried reinstalling macOS through recoveryOS, using another Mac to reinstall the firmware or do a complete restore to no avail. I even had a GeniusBar appointment for this case on in late July, where I brought in another MBP, and they verified that the second MBP added the cards to the Wallet just fine. I can't use that loaner MacBook from my work anymore, and I’m now left with a semi-functioning 16” MacBook.
I have been on the phone for more than 12 hours total with Apple Support over the span of a month, and the issue is still not resolved. After gathering some initial data about the issue, the Apple Pay Senior Advisor sent out a report to engineers on the team, who requested sysdiagnose and video recordings of the issue being reproduced. It's been two weeks since I've sent over the requested files and the Senior Advisors still don't have any updates. My understanding is that they have categorized this as a software problem, so there are offering no replacement option for me, no matter how long this process takes.
Last week, the Senior Advisor I spoke with told me to have “faith” that the issue might be resolved in 2 or more weeks with a 13.x or 13.5.x software update, just as they have "faith" that an issue they have with their HomePod will get resolved soon. Today, I spoke with another Advisor to see if there was any update, and once again was told that they wouldn't be doing their job right if they sent me another computer and it still didn't work, or they sent me a new computer before the engineers got back to them. In both calls, when asked about a timeline, the answer I got is that there is no timeline for such issues and I would be contacted if there was an update.
I appreciate the care that most Advisors dealing with my issue have shown, but I expected more direct solutions from the post-repair warranty and my AppleCare coverage. I have also filed feedback to the Apple Pay and Settings macOS teams (FB12952624/FB12952620). And to Jeff's great troubleshooting idea, I have contacted both third-party (Chase and Amex) and Apple Card support lines, and they said that there is no issue showing up on my account, and they tried removing the cards on their end but that didn't help. I also tried adding a card that I hadn't used before on that device and it still doesn't work. Interestingly, the terms and agreements page shows up but the usual card verification page (text or call) that many cards besides the Apple Card use doesn't show. I'm presented with the final "Your card was added successfully" page and when I navigate back to the Wallet page in System Settings I get the "Removed by issuer" error. When I called AmEx, they did mention that the card was being added only partially, without the verification step. Even when they verified the card on their end, the "Removed by issuer" error remained.