The critically important aspect: approach clearances and weather reports for a specific aircraft are still useful and relevant to all nearby aircraft. Narrow-casting them to specific aircraft reduces situational awareness for all other nearby aircraft. The system is also tolerant of noise: digital communications can be lost entirely with some degradation in signal, analog voice communications can still be interpreted with a fair bit of noise present (see video below).
The subtle aspect: multi-tasking by using more than one human sense - looking and hearing. People dealing with risky or dangerous situations absolutely should not be sucked into a screen for more than a minute or two to get critical information. This includes to more than one pilot where tasks are being managed and delegated. Most (if not all) controlled or 'aviator-coordinated' (CTAF) airports have a specific radio frequency to tune into to get weather information from an automated weather-to-voice system (e.g. https://youtu.be/HHbrlUPP-4k?t=339).
Whilst it sounds clunky, aeronautical phraseology (https://en.wikipedia.org/wiki/Aeronautical_phraseology) keeps communications detailed but brief and concise.
Digital voice communications often completely degrade for several seconds with a few lost packets, combined with the brevity of aeronautical phrasing can mean critical information is missed. All of these 'old' systems add up to the cumulative safety (https://en.wikipedia.org/wiki/Swiss_cheese_model) and doctrine built by the aviation industry over many, many decades though sadly because a lot of them were written in the blood of others who perished.