I wouldn't personally go so far as reporting my cards stolen once a year, but I could increase the security of my setup by having a checking account that all the things I just named access, and then having a second account that holds all my excess reserves, and transfer from the real account to the public account when things need to get paid.
Unfortunately, that negates most of the benefit of having things on autopay, like I do now. Besides, my bank actually treats my debit card the same way as the law treats credit cards (it's either max of $0 or $50 liability, I forget which), so it's entirely not worth it for me to go to these lengths.
I do this with most of my cards every quarter, staggering each card by about 2-3 weeks. Even ten years ago this level of opsec was practically impossible but nowadays I just log into the bank's app, tap a few buttons, and my digital wallets are updated with the new credit card instantly. I've got the process automated for 2/3s of my cards and worst case scenario, I have to walk from a store that doesn't support tap to pay to an ATM or major retailer for cash back.
Combined with Privacy.com linked to a secondary bank account for digital transactions, I'm feeling secure for the first time since I discovered online shopping.
If anybody can register themselves to that service, getting a new number isn't really a security improvement. Maybe somebody else knows more about that.