Also, iCloud+ allows the use of a custom domain. It may be an easier option for some.

I believe the major problem is having your email attached to a big tech general account. If your son decides to download a pirated game to your iphone, out whatever other unrelated minor offense, and Apple determine it's worth nuking your entire account, your email is gone. Granted, Google is worse at this matters, and when you own the domain at least you can point it to somewhere else, but it's still a hassle.

Does Apple have a history of doing that? This is the first time I’ve heard of that.

No

Even if that happens, it’s not a problem.

Why?

You go to your register and point your domain to another email provider, and you’re back in business.

Not a problem?

All your previous emails are lost, aren't they? Even you have local backup of them somehow, they are not equivalent to emails saved to your server?

Losing backups is problematic, but IMO the bigger issue is losing access. I care 10x more about emails that I haven't received yet, compared to my history. I am still not wanting to lose that history... but it is just not as big a deal.

The only way to cover that case is run your own mail server.

I've done that in the past, don't recommend it unless you have a real need and know what you're doing. It wasn't hard, but just extra work that I wasn't sure was worth it.

If you're using an email client, chances are you have an offline copy of your emails (depending on how you configured it)

If you have a local back up and the provider supports IMAP, you can just sync it back to the new provider.

Is it possible to recieve the icloud mail from a custom domain also in my non apple email app? For example on my desktop?

I recently switched things to an iCloud custom domain that I access through the Spark iPhone and macOS apps. It’s been an upgrade, though I’m still in the stage of finding and switching over accounts that use my gmail. I feel like that will never end.