This isn't Jagex being incompetent, this is Jagex's security improvements for Jagex Accounts hard at work keeping player's accounts secure (and in this case, not working the way you wish they would).
Part of the drawback to older RuneScape accounts was that Jagex would manually intervene, which could end up leading to the wrong person getting access to an account they do not own.
With Jagex Accounts, they're taking the other, more secure approach - everything you would need to change can be done from within Jagex Account Management by you, and they are not manually intervening at all. Of course, this expects that you are able to log into your account in order to make those changes. They expect that the user will always have access to their email address.
Jagex's policy on no longer being able to access your email address is outlined clearly on this page: https://help.jagex.com/hc/en-gb/articles/12605217736593
They state,
"For the sake of optimal account security, we're unable to modify your Jagex account email or disclose it to you."
In the situation you were in, if you had enabled app-based authenticator, you would have been able to get into your Jagex Account to change the email. However, if the only thing enabled was email based authentication, then you would need to retain access to that email account to retain access to your Jagex account.
There really isn't any advice players can provide (or anything Jagex can do) to help here - if Jagex intervenes, they undermine all security benefits of Jagex Accounts, which would be a very bad thing to do.
20-Jan-2024 15:48:04