The EU legislation allows "opt out" from level 2/level 3 notifications, but is based on the notion that messages are received "without the need for the public to have to opt-in".

So for compliance sake, you're opted in. Maybe this should only happen the first time you enter EU or a member state, and then either your phone or cell service provider should remember your preference (which is probably not worth the resources to implement for the cell service provider, but maybe your phone already does?).

I'd be interested to see if this already exists, i.e. do you only need to opt out in Germany once? Does that opt-out at EU level?

When your wife disabled notifications, she merely opted out of notifications in whatever jurisdiction she was in (presumably US?), but opting out of something in US doesn't mean you opted out of every other similar law from every other nation state.