My understanding is that air traffic control is extremely computerised even though direct control is still done over analogue VHF voice radio. The flight numbers are essentially only human-facing (both passenger flight numbers, and ATC callsigns). When flights are handed off between different stations or different flight information regions, their computer representations must conform to the Flight Information Exchange Model (that's the FIXM in the website I linked above).

It's a very top-down initiative by ICAO and all the large aviation authorities—quite unlike the rest of the software development industry.

Frankly speaking ATC is the only thing that really matters in the context of flight safety—ticketing, terminal operations, etc don't (and don't need to) deal with FIXM.

Like the mechanical displays at various airports across the world pictured in the article?

Overall seems like a project of huge size and somewhat unknown reach. Not my domain, but I would imagine all kinds of ground support systems to have the four letter flight numbers baked deep into their assumptions. And not only direct support like fuel, cleaning, work shift scheduling, but also logistics systems for cargo, military systems, myriad of ticketing systems etc.

So we’re already too late by about 20 years to fix the issue properly.

Undoubtedly we’ll push the issue forward for another 10 years before realizing that the next best time to start was today :/

4-digit flight numbers are for humans, not computers

But humans, who interface with computers, are known to cause trouble.

Humans write the code that makes those computers do things, though. And humans don't always read the standards, docs, or manuals before doing so.