I can believe that they would convince her. But steel manning her argument should go no further than having her point out what you just said, and should not include adding unrealistic or unusual evidence to the story.
And that's if it is indeed a strong thing to point out, but even if some ponies will still choose death, alicorns can easily avoid watching them. There's nothing to say an alicorn has to hang out with non-alicorns. (The most deaths an alicorn might see in waiting for their non-alicorn friends and family to die off is probably less than the amount a particularly long-lived human might see, and I've never heard of an centenarian who stopped caring about everything because of witnessing deaths.) If non-alicorns were still choosing death all throughout the future, their deaths could be mere faceless numbers to alicorns that didn't want to think about it. Much like the millions of humans dying today in real life, and the billions who have died throughout history don't emotionally traumatize me.
Actually, I can respond to the biggest reason why I wanted to introduce someone broken by immortality inherently: "There are no such people, because I have carefully avoided creating them. It would be the most irresponsible thing imaginable to cause someone to suffer such a fate!"
I recently published Mortal, a novella-length My Little Pony fanfiction meant to introduce anti-death concepts to an unfamiliar audience. Short description:
This is a character-driven melodrama. It's not particularly rationalist, but it's very, very transhumanist. Unlike, say, Friendship is Optimal, I wouldn't necessarily recommend this one to people who don't already know the source. It assumes familiarity with the characters and the world.
I am going to talk about how I put together the story and how people reacted to it. This will contain spoilers.
This line exists so you can break out of the automatic "read everything on the page" mode if you want to avoid the spoilers.
This story was structured as something of a bait-and-switch. I watched the reaction to a previous transhumanist horsefic (yes, there's more than one), and I was struck by how easily readers matched the explicitly anti-death narrative to the "immortality is a curse" trope. Rather than fight against this trend, I decided to work with it. The first act is meant to look like a story about learning to accept the inevitability of death. Starting in chapter 3, I break further and further away from that mold until the protagonists finally rebel against the status quo.
The first chapters got a lot of people invested who I suspect would've been turned off by a less familiar opening. Once I was into the third act, I stopped being subtle and used every trick in the book to make the pro-death characters look like the unreasonable ones. Judging by the comments, there's no shortage of readers who were angry at having their expectations flouted, but quite a few seem thoughtful, and some explicitly changed their mind on the subject.