The risk with Gmail is not about Gmail shutting down, it’s also Google shutting you out.
Several years ago I went to login to my gmail account and couldn’t. I knew I had my correct password in 1Password, but it wasn’t working for some reason.
I finally got to some page (I don’t remember what specifically) that said “Your account has been suspended.”
Looking up what I could do under those circumstances, the answer was “If your account has been suspended, the decision is final. There is no appeal process. We are not obligated to tell you why your account has been suspended.”
I knew that I had not done anything that warranted having my account suspended (I was barely using it except for some mailing lists, etc).
It took a week, but I finally got my account re-enabled by jumping through 4,732 different hoops and responding to emails from nameless/faceless Google employees who seemed loathe to help.
No clue was ever given as to why my account was suspended. It was suggested that the process was somehow automated, so it wasn’t even a person who decided to suspend my account, it was some kind of Google bot.
If you aren’t a paying customer, if there is no customer relationship and no one to contact if something goes wrong, you are risking losing access to your email account. Not just with Gmail, but with any of these free providers.
Now, think about what goes to your email. Think about trying to access your accounts and services without being able to access your old email accounts. Think about how many of them won’t let you recover a password if you don’t have access to the email account on file. Can you change your email address on all of your services if you don’t access to the old email address?
Now, imagine this…
Pick a domain. Pick an email address “you@somewhatever.whatever”. Use that email address for everything. You don’t even need to manage anything, you can even just forward it to a Gmail account if you want.
Then one day you realized that Google has shut off your Gmail account.
That same day, you can either setup a new Gmail account or use a different provider and start forwarding “you@somewhatever.whatever” to the new provider. If you don’t have backups of your old email, you might lose access to those messages, but you’re never locked out of any of your accounts because those accounts are connected to “you@somewhatever.whatever” not “someone@gmail”
“Well, I’ve never heard of that happening to anyone else…”
Sure, I’m guessing 99% of Gmail users will never have to deal with that scenario I described, but when you find yourself in that 1%, it’s little comfort to know few other people end up there.
I still have an use a Gmail account,I have daily backups of it, and I don’t use it for anything crucial. It’s my generic choice for “This site requires an email address” especially if I don’t care about that site. But for accounts that I care about, especially things like PayPal, banks, etc., I would never use an email address where I did not own the domain.
FWIW.