Haha, LET ME TELL YOU ABOUT TRANSFORMATION FICS. Because I certainly don't have an example of one in my sig or anything.
To answer the questions in order...
What makes human-to-Pokémon transformation fanfics unique?
Is "everything" a possible answer?
Okay, but seriously, to answer this question, let's start off with a short recipe for a TF. Take one human -- preferably ordinary but it's not like I've ever taken a special canon character and transformed the **** out of him or anything. Add one science experiment gone wrong/spell/hidden genetics because your mom had her way with Mew/what-have-you. Combine species-related angst and suspense. Beat until soft peaks are formed and then bake at 350 degrees for-- oh wait.
Point is, while TFs do have a certain formula (when they're not plot-what-plot porn), it's really unique among Pokémon fics because the formula is extremely broad. So long as that human turns into something that isn't human and shenanigans ensue, you can literally do whatever you want. It doesn't even matter how that happens. You can have a reborn fic (human dies and is reincarnated with all their memories intact as a Pokémon), and that's TF. You can have a plot where Team Rocket kidnaps your main character and turns him into a Pokémon, and that's TF. (No, really, I swear to God I'm not describing just AEM there.) You can even have a character willingly do it to themselves for whatever reason. The sky is literally the limit.
But on top of that, with most TF, you have the option of making a story that's extremely deep. Sure, you run at a risk of making something exceedingly and hilariously pretentious, but if you do it right, you've got things like "What is a human?" and "Racism: not just for people anymore." The problem is that not a lot of people see it that way for some reason, so they just get stuck on the "LOLOLOLOL MY CHARACTER TURNED INTO A POKEYMAN" bit. Not that stories like that aren't good, but it's always fascinating to see when people remember -- even vaguely -- that transforming from species to species is not something that happens all the time and include that in their fic.
And I could really go on and on, but lemme try to keep this from becoming a novel, amirite?
What are [your] responses to these kinds of fanfics?
I definitely prefer writing them to reading them for a reason I actually mentioned earlier. (Not a lot of people write a story that's more than just "human turns into a Pokémon, and absolutely no implications of this are ever explored.") But even then, it's not like my cynicism to trainer fics. I won't sigh and go, "Oh God, it's another one" to a TF; I will read the crap out of every single TF you give me. The crap out of it.
...Unless it's a reborn fic. Reborn fics are like the trainer fics of the TF world. You have a handful of supposedly good ones (I say "supposedly" because we won't get into my opinions on the original.) and tons of knock-offs that are basically cookie-cutter because the authors are attempting to cash in on an idea that's popular. They... generally don't turn out that well-written. [So you have to look particularly interesting, new, and different for me to get into your fic.]
Does it remind many fanfic readers that they're too furry as to why a human would give up his humanity just to become a Pokémon?
Lemme rephrase this question to something I think you were asking: "Do people think it's just furry fic?"
The answer is: It depends on how well-written it is and what the plot is. In my experience, not that many people would turn away from a TF just because they think it's a furry fic; in fact, the furry part doesn't even cross their minds. It's really the people who have no comprehension of what the genre is who assume that it's all furry porn or whatnot, if I may be blunt for a second.
Of course, that opinion varies. There's some TF out there that's pretty obviously furry fic, with the character being excited that they're Pokémon. Those tend to be less-than-well-written (or outright PWP porn). The fics that are decent to well-written, meanwhile, are generally ones where the character isn't willingly giving up their humanity, so it's more of an exploration of deep philosophies/hilarious shenanigans than just something to satisfy the writer's furry itch. (If they even have one. Some of us aren't even furries to begin with, not that I have any problems with furries.) That isn't to say that you can't write a well-written fic in which the character actually wants to turn into a Pokémon; it's just that it doesn't really happen that frequently. If you did, sure, you'd get people saying it's furry fic, but so long as it's well-written, I don't think many people would care. Especially on Serebii, where you don't actually have to mention that it's a TF of that nature right away (because there's no summary field and because you don't have to write that so that it appears when you hover over the story's link).
What are the challenges [of] writing a human turning to a Pokémon fanfic?
First and foremost, like I said, you have to remember that this is weird. This is weird to the victim character, this is weird to the people around them, and this is weird to their entire universe. Once you have that in mind, go right ahead and do whatever you want.
But seriously, keeping in mind that this is going to strike the characters as weird eliminates a huge number of issues the average TF faces, the least of which being the implications of being transformed. (As in, do they face prejudice? Will they be hunted down? Will they have crises wherein they start becoming more Pokémon than human? How do they feel about that? Are they terrified of losing themselves? Are they terrified of being captured? And so on.) This goes especially if the character turns into a legendary or part-legendary.
The other issue, of course, is making the transformation to -- and possibly from -- believable and not-so-cookie-cutter. Like I said earlier, TF follows a broad formula that can be taken any number of directions, but a lot of TF authors tend to fall into a trap where they just write the same fic over and over again. On the sci-fi side, it's "teen gets captured by Team Evil (usually Rocket), who experiments on them for no discernible reason until the teen transforms into a half-Pokémon/full Pokémon and escapes." On the fantasy side, it's "teen gets cursed by item/legendary Pokémon, turns into a Pokémon themselves, and goes on an epic adventure involving a prophecy and saving the world in order to change back." The sci-fi end of things tends to be particularly cringe-worthy because the author sometimes fails at offering an explanation to anything. There's no science, there's no reason for Team Evil's actions, and there's no point to why that particular teen got captured. So the beginning just feels like it's a rushed jumble of loose plot to get to the part that satisfies the author's kink interests, especially if the rest of the story can include the words "is running from Team [Evil]" in its summary.
...And, of course, if you're going to make a sci-fi TF, you'd better actually involve science, y'know?
And I could go in-depth about the philosophy that you could cover with a TF, but the truth is that you can do that subtly as a secondary idea. The other trap a TF falls into is it focuses too much on the philosophy aspect of the concept and becomes insanely pretentious. Extra points if one or more characters exercise sesquipedalian loquaciousness. To avoid that, just remember that the more you force yourself to seem intelligent, the more you look like a tool. So the real challenge in exploring any philosophical theme in your fic is working out the concept of subtlety. I encourage you to explore all the philosophical bits, the social commentary, and what-have-you. In fact, that's the entire reason why I said, "Remember that this is going to be weird to the characters." It's just that you shouldn't beat the reader over the head with the idea that this work is going to be ~deep~ at the same time. It's all about finding a balance between remembering the weirdness/its implications and making the story not be something a teenager who thinks they're a genius would write.
But I'd be totally up for actually discussing the philosophical bits too.