That reason is to let people know the content rating of the story they are about to read. Should it be rated T, for Teen, one should expect, as laid out in the rating system used by FFN (link: www.fiction ratings.com), any or all of "some violence, minor coarse language, and minor suggestive adult themes". This is noted as " suitable for teens, 13 years and older". You can read the rest yourself; be aware that FFN uses K, K+, T, and M, but *not* MA (although, to be fair, some posters do blur the lines a bit between M and MA. Many others, however, will post the MA/NC-17 scenes they write elsewhere, so as not to violate the terms of use).
The youngest age you can be in order to have an account on FanFiction.net is either twelve or thirteen. A four-year-old--and you're assuming a four-year-old who knows how to read pretty well, not to mention find the site and navigate it--well, even assuming a young child who's been shown the site or something, that child should either know or will quickly figure out that they should stick to the K or K+ rated stories, of which there are many.
In my experience, users of FFN read stories at a rating with which they are comfortable. The only main 'dangers' are mis-rated stories or first-time users who haven't figured out the rating system yet (although, even then, M-rated stories are not displayed by default). To the first: I have every confidence that should Bramandin post this story on FFN, it will be correctly rated--or even overrated for safety, as is common practice. Should a reader too young for the themes find it, read it, and, of course, *understand* what it's getting at--and young readers miss many things that older readers get, due to the difference in life experience and so on--well, that would not be on the author, assuming the story was correctly rated and the trigger watching included in either the summary or an opening A/N.
FFN, and other sites, are filled with all sorts of stories. Some are good; some are thoughtful; some are bad; some are horrible. They come in many genres. This is no less true of children's shows--see My Little Pony for one example, or Kim Possible, or just about anything.
Also... I don't belieof that anyone, *ever* has sued a fanfic author for writing a story a little above the rating level of a person who read it, especially of their own free will. Moreover, the *only* thing Bramandin has warned for is "off-screen child abuse". Trust me--there are much, much, *much* worse things that have been written about in both fanworks and original works. Honestly, from the information we have, I'd expect this to be a thoughtful sort of piece, a different take on something or else a 'what if this character was confronted with this issue'.
Also? As far as I remember, there's child abuse awareness stuff (campaigns or education or something?) going around, so as to teach kids to speak out about it. Assuming it's even more than a minor sort of thing in this piece, it would probably just feed into that, at most.
tl;dr: FFN, as well as most sites, has a rating system in place. It's linked above. Rating correctly is the responsibility of the author, and putting trigger warnings in is considered considerate everywhere. (Archive of Our Own even has those as warnings in the rating system). Reading at the appropriate level, however, is the responsibility of the reader and of the people around them--*not* the author. Bramandin's piece also does not seem to fit the category of 'absolutely traumatizing'; moreover, Bramandin clearly knows what to warn for. Also, fanfic authors generally do *not* get sued for things like this; much more likely is, at most, publishing a fanfic as their own book without authorization or changing names, etc (ie, if EL James had published 50 Shades without changing the names and without getting Stephenie Meyer's permission to publish a Twilight tie-in or something).
In short: I see no problem here, nor, in fact, anything remotely unusual. I'd also suggest actually reading the piece before condemning it; it really does not sound to me to be particularly traumatizing by most standards, and the author's comments seem to support that.
If you'd like a run-down on AO3's rating system, I can do that. It's a similar sort of concept, but with different terms and with tags. Tumblr, meanwhile, has no rating system whatsoever, just the option to use tags and the stipulation that... 13, I believe, is the youngest age to have an account. FFN or AO3 is really a better bet, especially if you want to know the content rating quickly instead of guessing from the beginning or the tags--which won't always be there.
Also... Tumblr hosts stories, yes, but it's not a fanfic archive. That's not its official, main, or primary purpose. It doesn't really make as much sense to post stories exclusively to there.
And, right, I'll finish there. Apart from adding that I've been with all of these sites I've mentioned for a while: FFN since 2009, though I was reading there earlier; AO3 since at least a few years later; and Tumblr since 2011 or 2012 (probably 2012).
Thanks for reading.
~DF