There should probably be separation between dysphorics and non/sub threshold dysphorics.
I mean, ostensibly there is -- you still need a diagnosis of gender dysphoria to take hormones on taxpayers' dime in most developed countries. The issue is that the signs are embarrassingly vague and fail to really add up to anything. All it really takes is six months of wishing you were the opposite sex, whatever that means.
Even if you were to police things harder, though, on what criteria could you distinguish a "real" dysphoric from a fake one, especially now that the cat's out of the bag and everyone can Google up a handy checklist of symptoms? Many straight AGP types do experience genuine discomfort with their sexed characteristics, often moreso than the naturally-effeminate neurotic homos to whom the "true transsexual" label allegedly applies (this is pretty much a new invention, btw; Ray Blanchard recommended that autogynephiles transition in the 80s, and they were doing it for a long time beforehand). So you can't really use gender-related distress as a metric. Age-of-onset is dubious and easy to misconstrue/make up entirely, so that's out of the question too.
Not accusing you of anything, but I get the sense that when people talk about separating "dysphorics" and "non-dysphorics", they really mean palatable trannies i.e. passing/semi-passing femfags who already seem a little strange as men, and unpalatable trannies i.e. Reddit atheists turned transbian beasts of righteous honrage. Dysphoria doesn't mean anything, really; it's a state of mind you can stumble into from an infinite number of angles.
There could be some merit to transsexuality as a condition distinct from GD. It's got nothing to do with having an opposite-sex brain, though.
Honestly, if they really want to maintain access to transition legally, it'd be best to make an appeal to one's natural rights (bodily autonomy/freedom of expression) rather than something contentious and disprovable (medical necessity/gender identity; as well as it not being something broadly applicable to all trans people).
Nobody's going to believe that now; the category is tainted. Not that it was ever
really about bodily autonomy in the first place.
You're probably right in that the irresponsible talk about suicidality is actually making trans people and children who think they might be trans suicidal or more suicidal. Iirc, if you speak about suicide in a certain way or report on it without certain considerations, it can cause a large uptick in suicides.
You can see it in real time when they happen. There was that TF2 modder who jumped from a bridge in Portland or whereverthehell and /lgbt/ was flooded with suicide posts for weeks after.
I actually respect how the Sharty kids responded to that one, even if it was pretty horrible in a vacuum. It's probably the first time that particular narrative has been countered on such a large scale -- "no, you won't be a martyr, we're going to tape soyjaks to your memorial site and make fun of how you didn't pass". The best way to stop teenagers from roping is to make it desperately uncool.