Mail is the lingua franca of the Internet. There are many, many alternatives to just getting an account with one of the handful of well-known huge providers and being locked in to whatever they want to do to you afterwards.
Just about any ISP will provide the necessary servers to send and receive electronic mail.
Plenty of hosting services will let you keep your own mail store in a remote, always-on location.
Either of these also works fine with your own domain with any decent provider, and either costs a modest amount to run for something so important and useful.
If you are limiting your options to a specific type of webmail service then of course you're going to be stuck with whatever downsides that comes with, but that's far from your only option.
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¹) On a leased hardware, network and address, but with proper backup and failover strategies, hosting providers are interchangeable (or one can always host on their own hardware) and it's somewhat less likely ICANN or your local registrar would yank your domain name registration than Google would do so to your account.
²) There are (nearly) one-click solutions for this, like https://cozy.io/ or https://sandstorm.io/
I'm pretty sure Gmail is the best free provider, but Fastmail is probably the best paid one.