Peri is the most mishandled companion in the entire show
The fact that she's so close to being an interesting character and then ends up just getting captured every episode is so frustrating. Any of the identity Peri has is due to the actress, Nicola Bryant, literally having to write her own character's personality and backstory because they never gave her anything. Much like Colin Baker, Nicola put all of her effort into a show that didn't care about her.
When talking about the material the show gave her, JNT saw the success of The Caves of Androzani and decided to make Peri suffer more than any other companion in the show up to this point. He explicitly stated that the only purpose of Peri was to be a sex object, and what we got ended up being toned down from his original vision (making her wear bikinis and leotards the whole time). Regardless, Nicola still ended up getting sexually harassed around the studio.
The 6th doctor's bold personality requires a companion with a personality that plays off of it. Say what you want about Mel but at least she has a consistent character that clashes well with the doctor in the form of being a bubbly optimistic inversion of him, and once the writers just fully embraced the screaming child idea it actually looped around and became entertaining. Peri and the 6th doctor are incompatible and this is one of the major reasons for the show's quality falling off a cliff as soon as The Twin Dilemma hits. Both characters are murdered as far as writing goes in 6's first story and they never recover. I actually don't hate where they were going in theory with their characters in that episode but if you don't have the writing skills to pull it off you get... well... that.
A few previous companions had good basic character arcs (e.g. Adric, Tegan), but the writing always left something to be desired. There was so much potential for something interesting with Peri, and none of the writers gave a shit. In the end, the show doesn't even bother trying to explain what happens to her. If you add in the Big Finish stuff I think there's like 5 different explanations.
At least the classic run of the show ended up getting a well-written companion at the very end.