Imagine all the normal people who can not run their own mail server and do not have the paranoia or the time to set up 3 of everything and never miss the periodic chores to keep them all alive just to guard against one of them being cancelled. You certainly don't want anything important like your retirement account to rely on something transient like your isp email, or even a paid email from some smaller company that…
I would absolutely not consider a free account on anything to outlive a paid product. Quite the opposite: If I'm not paying for any kind of SLA, written in an agreement, I assume the account in question is temporary, could disappear at any moment, and treat it as such: Never rely on it for anything where you'd be screwed if you suddenly got locked out.
There have been so many, many, many, many of these "I got locked out of my free Xyz account with no appeal possible!!" stories, I'm shocked that people still rely on them. And if you say, well, you shouldn't have put your 401(k) retirement account behind that E-mail address, they call you victim blaming. People, your free account is worth what you pay for it.