Even if you have alternate email addresses associated with your iCloud account, you are free to update it to have your external email address be the default for your iCloud/Apple ID.
Although I will note that it says you can't change your Apple ID email address if you choose an @me.com, @mac.com, or @icloud.com email address for your Apple ID, which is the first time I've seen that warning.
Visit https://appleid.apple.com/account/manage to make those changes.
Help article: https://support.apple.com/en-us/HT202667
Although I will note that it says you can't change your Apple ID email address if you choose an @me.com, @mac.com, or @icloud.com email address for your Apple ID, which is the first time I've seen that warning.