There does already exist a system for ATC to send info to Pilots via text. Particularly used when in heavy-traffic areas to limit the amount of voice communication.
CPDLC https://en.wikipedia.org/wiki/Controller%E2%80%93pilot_data_...
CPDLC https://en.wikipedia.org/wiki/Controller%E2%80%93pilot_data_...
Isn't approach one of those times where 1) you don't want the pilot distracted by more visual information (instead of audio), and 2) pilots listen to exchanges with other pilots to keep situational awareness?