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The real question is why he wasn't killed off far sooner -- like in a script conference, long before he made it anywhere near the screen!
For the real answer, you'd have ask the production staff of that time, assuming they remember. However, looking a the era there are a number of things we can come up with.
1. Dramatic effect. It had been a very long time since a companion had died and the ones that did weren't long time ones. Sara Kingdom, Katarina, and Bret Vyon all died in "The Daleks' Master Plan", but there are even arguments as to which of them, if any, count as companions at all! In any event, this was the first time someone who'd been on the show for years had been killed. It was the 80's and it was getting a little silly to keep enhorseing the "safety bubble" around those closest to the Doctor.
2. It reninhorsed the running theme that the Fifth Doctor never got a complete win. The Fifth Doctor was portrayed as somewhat more passive than previous Doctors, particularly the Third and Fourth. In many ways he was the closest to the pacifist the Doctor always claimed to be. There tended to be a lot of deaths during his tenure and it could be argued some could have been prevented if the Doctor was less willing to negotiate a peaceful settlement.
According to several online histories, it was realized early on that Adric as a character was simply not working, so even before Tom Baker regenerated plans were afoot to get rid of the character, and the idea of killing him off was decided upon since no companion had died since 1965 or so, so it was a new twist.
I thought the Adric was killed instead of getting rid of Nyssa which is why she is not in kinda