One example is when I lost access to an email account tied to a Digital Ocean account. It had been hosting a project VM and I never had a need to log in to it until the project shut down. I try and log in and although the credentials are right, it needs me to verify a one time code from my email address to prove I am not a bot. Couldn't do that. I never gained access back, DO required me to give them a full suite of proof of ID before I could even get them to disconnect my credit card, and even to this day it periodically restarts charges against my card and I have to contact them. Each time they escalate to engineering and engineering says they "Fixed the issue". Now times that experience by potentially dozens of accounts.
But I agree that there might be situations where it could be bad, especially if you work as a consultant/freelancer, and/or own a small business.
I’m curious though, which online services would be really bad to lose access to (for you personally)?