I've never heard of any kind of INFJ envy or misrepresentation. Is that a thing? If so, why is it a thing? I don't think INFJ would be desirable. Maybe in some circles.. but I think people would much prefer the outgoing, risk taking types. I've been divorced for a while and tried online dating and everyone for a while was posting their MB types and I never saw an INFJ, even though I am one. Maybe for bookish, nerdy types that are still stuck in a highschool mindset, INFJ may be appealing but from what I've seen in the adult world, it really doesn't seem to matter a lot and it's not desirable. I don't mean anything derogatory by remarks, I'm just seeing stereotypes in my head and I think the whole idea of people trying to define themselves by a label is a bit bonkers.
It's true that now that MBTI is more and more popular and a lot of people just take the test and post the result on their dating profile, the majority is not going to claim to be INFJs there. I've also been on one dating+networking site and INFJs are not that common.
In MBTI enthusiast circles there's still a trend though. I only have a theory of how that came to be. Carl Jung, the father of the cognitive function system has been widely agreed to be an INFJ, and I think maybe that's one of the reasons there might be a slight bias in favour of INFJs, in the history of the narrative that surrounds MBTI. (Like there is a negative bias toward INFPs though I have no clear theory for why that happened...) The other more obvious reason is that INFJs are, according to most sources, the rarest type, and there are a lot of people who are attracted to that sort of lable. Indeed, if they understood what INFJ as a type really means, they probably would not particularly desire to be INFJs. They don't actually want to be what INFJs really are, they just wish to be celebrated for whatever it is in themselves that they associate with being an INFJ. (And they are, or at least used to be, so much less likely to be celebrated if they identified with another type with a similar vibe, especially INFP.)
Also, the original internet typology community was probably mostly NT, NF, or introverted types, and while it may be true that at their core those types would actually desire to be more active and outgoing types, most of them were probably self-aware enough to know that they did not belong to that kind of personality type. They knew they were bookish, nerdy, introverted and "deep", so it made more sense for them to identify with a type that was celebrated for these qualities in the typology circles, than to go for the
obvious lie that labeling themselves as ESTPs or something, would've been.
This is a simplified educated guess.

I'm sure I could spend a whole day theorizing about this. But the reason I brough it up in the first place was because it's so similar to this trend where people want to have been well-known in their past life and don't
really understand what it is about. They don't understand it isn't "cool", any more than an "unknown" life, likely even less. Being an INFJ is pretty much the same in this day and age. (I guess people never stop to think that INFJs must be rare for a reason... and it isn't because we're special. It's more likely because society at where it's going doesn't benefit from large numbers of INFJs like it benefits from large numbers of ISTJs for example.)
I could've come up with a more simple parallel if I had thought of it at the time: I have a friend who talks and talks about wanting to be a "good person" and to help people. However, he's so attached to the label of being good and doing good deeds that he never actually does any, because he thinks it's supposed to feel glorious somehow. He passes by almost every opportunity to help a friend or a stranger because those situations don't fit with what his ideal of "helping" is. He's so attached to the idea of being a helper of mankind that he doesn't realize that helping people consists largely of getting out of one's own comfort zone: it's work, work you do because you care about others and not your self-image. He turns down almost everyone who ask for his help, and yet he still manages to have this idea in his head that he is a helpful, selfless person.
I think similarly, a lot of people just don't realize what the life of that historical figure they so admire or identify with, must have been like, because things can look so much better and simpler on paper, or in vague fantasy, than they really are. People like to glorify hardships, but very few would actually do what their personal heroes did, or understand the real reasons behind those things.