NDB stations, an even older type of radio navigation beacon, also broadcast their identifier like this. I fancy they might even outlast VORs due to how much cheaper they are to operate. The real survivor though might be the ILS (Instrument Landing System): ILS transmitters broadcast their identifier in Morse code, as did the prototypical Lorenz systems, making them very nearly a century old already (Lorenz systems were first installed in the 1930s). ILS approaches are the most common type for commercial aviation in most countries.

The one navaid likely to be around for the foreseeable future is DME. Which sounds slightly strange if you know a bit about aviation, you probably know it as slightly subservient to VOR as in VOR/DME. However, taking a number of DME fixes is a common (though slightly outdated) way of updating a fix for an aircrafts inertial navigation system.

I think a minimum viable VOR network is planned to be maintained as a backup to GPS.

Indeed; Eurocontrol have published a handbook about it: <https://www.eurocontrol.int/sites/default/files/2021-10/euro...>. Here's the USA's Federal Aviation Administration's page on the topic: <https://www.faa.gov/about/office_org/headquarters_offices/at...>