Oh, I can't believe I missed that the poll listed using references in Fakemon, I actually really like seeing those! InvoluntaryTwitch has some really cool Pokemon in Uranium that reference the Hatoful Boyfriend game (the Masking line and Antarki), and I also loved her Psychic-type Pokemon that mixed in Gravity Falls with the Illuminati conspiracies and that triangular prison. (the name's escaping me for now) I've also seen some really neat UBs that referenced Mario and Sonic in their designs-I couldn't figure out how they were inspired at first, but after reading the artist's comments, I could see the influence in the Pokemon, and it was really fun to notice the little details!
To me, referencing some form of media in the design of a Pokemon doesn't seem too out of the ordinary-stories from the past make their way into Pokemon designs, after all-but I do think that it has to be altered a bit to be made into a Pokemon. Not major changes, but just a little change to the lore about them so that they seem like a Pokemon instead of a guest star. (and maybe a slight art style change if it seems a bit out of place) For example, suppose you wanted to make a Fakemon based on Crash Bandicoot. A bipedal Pokemon in shorts and boots is obviously going to stand out, but making it a quadruped like actual bandicoots and removing the clothing would make it look more like a Pokemon. And you could make plenty of references to gameplay with Pokemon elements-it could learn moves like Bounce and Rapid Spin, could have some ability making use of berries (referencing the Wumpa Fruit), and its Dex entry could make some remark that it often enjoys smashing crates.
Memes could be used to develop Fakemon, but I don't think a meme alone is a basis for a Fakemon. I think a Fakemon needs a more solid foundation than just a joke everyone knows, especially since those don't often mesh immediately with the Pokemon world. But combining a meme with a more interesting origin could make for a fun design-even if it gets a few groans.
For example, the "That's none of my business meme"-if you just gave a frog a teacup, that wouldn't be much of a Pokemon. But if you add in some other elements, the design could become more interesting. Suppose we added in Tasseomancy (tea leaf reading) and gave the frog something more natural for its environment, like a lily pad cup with water lily petals as the tea leaves-that could be a stronger foundation for a design. (and if you really wanted to make sure people got the meme, the dex entry could say something like "This Pokemon can see the future in the remains of its drink. It doesn't share this future with anyone, however-that's none of its business.")