I was lucky enough to get it again. This time by just starting a mission during a session of ~100 minutes. Still no clue as to why this happens exactly. This glitch seems to have more to do with voicelines not working properly instead of just the radio function itself. This time I took the time to explore its side effects more thoroughly.

General

• Kaz and Morpho cannot communicate to Snake with the codec. Small talk between guards will have the voicelines missing but will still play their talking animation.
• Cassette tapes are unaffected, as is interogating guards.

Cutscenes, game overs, debriefings and mission specific stuff:

• Most cutscenes are unaffected. Game overs (and result screens) have no voicelines. Debriefings have no voicelines and will not progress until skipped.
• Intel Operative Rescue cannot progress past the communication tower.
• The 'open the frontgate' cutscene in Ground Zeroes has no voicelines and the frontgate takes significantly longer to open.
• On Destroy the AA's, the guards will still automatically enter alert phase. The airstrike cutscene plays out like normal.
• On Classified Intel Acquisition, the bald guy is unable to give you the second tape. The cutscene in which the target tells Snake the location of the first tape plays out like normal.
• On Déjà Vu, the background crowd noises during the debriefing will play on cue but the voicelines are missing and the briefing will not progress until skipped. Choosing to take on the mgs quiz will completely softlock the game. I couldn't test refusing the quiz due to this. Snake also doesn't comment on certain scenes when recreated.

Guards and CP behaviour:

• As a rule of thumb: radio calls between the guards and CP actually take place but are severely lengthened, taking multiple minutes to finish. The actions and phase changes associated with those calls are thus heavily delayed. (for example: spooking a gaurd by shooting near him will still cause an alert phase after a while that will eventually revert back to normal phase.)
• It is still possible to Interrupt the radio call by tranqing, injuring/killing or throwing a grenade near the guard that's making the call. Most of the time, another guard will simply make another lengthy call.
• Combat phase is kind of messed up. After being discovered, the guards will open fire and will cease fire after escaping sight for a while like normal. After that though, guards enter combat phase a second time (when the elongated radio call that happens upon being discovered has finished), briefly opening fire at Snake's last known position before ceasing fire again. After that, they hang around Snake's last known position for a while before reverting back to alert/search phase.
• Enemy reinforcements will still appear like normal if too many losses are taken during combat.

Final note: I forgot to test about shining the Kojima Productions spotlights and erasing the metal gear logos. Another time I guess.