First, I gotta correct you on one thing: The stigma hasn’t been removed. It’s as alive as ever. In fact, it’s an indirect part of the answer to your question.
There may or may not be an increase in the number of cases of mental illness recently as compared to less recent times in memory. It may be that more people are being diagnosed or more people are recognizing the signs of mental illness in themselves. There was a time when most people with certain mental illnesses were just given descriptions like “high strung”, “asshole”, “criminally minded”, and so forth. On the other hand, there may be people who today are high strung, assholes, criminally minded or something to that effect who feel they match the symptoms of a mental illness but would not actually qualify for the diagnosis. Then there’s the point where psychology meets sociology: Culture and society play a heavy role in the development of our psychological makeup. It’s entirely possible that as our world becomes ever more uncertain and hostile, more people develop psychological problems. There isn’t as much research done on that link as I’d like, but it does seem to be gaining momentum.
There’s also the fact mental illnesses are the easiest illnesses to fake. There are people who seek attention and sympathy by claiming some kind of illness that they don’t have. There’s actually a psychiatric diagnosis for this, but it’s not generally one they want to claim. But since there have indeed been some efforts to get rid of stigma to the point that it’s becoming more acceptable in some situations to admit that you’re mentally ill, claiming a mental illness of your choice isn’t too hard and the deception can be hard to detect by a mental health professional. Nothing can really be done about that, but there may be a chance that as more and more people become open about our illnesses, particularly famous people, more people will make the claim.
Related to that last part is how we seem to occasionally go through periods where one mental illness in particular kind of gains some kind of popularity, leading some to believe or claim that they have that illness. This often happens when there’s someone who feels different from others and possibly alienated, so this mental illness which is gaining some amount of sympathy in the public eye while retaining a luster of mysteriousness is again an easy thing to claim. Dissociative identity disorder, multiple type, or multiple personality disorder (the old name, though some prefer it), got a big boost in 1976 with a television miniseries starring Sally Field titled “Sybil”. That diagnosis is still a bit controversial, but generally accepted. However, after that miniseries, there was an explosion in diagnoses that lowered over time when people started forgetting the miniseries. Probably many of those were legitimate, but how many is impossible to say. The fact that new diagnoses died down later suggests that some may not have been. This has happened a few other times but most recently seems to be showing its head with sociopathy (which is under the umbrella of antisocial personality disorder) because of the popularity of the show Sherlock. Sherlock is portrayed as intelligent and the actor is apparently considered very attractive to many people, and the character is portrayed as being a sociopath. Suddenly every loner that’s into the show thinks they’re a sociopath, having no concept of what a sociopath really is. There is plenty of evidence of this right here on Quora.
It could be any of these or some combination. It could also be due to something we couldn’t begin to guess at the moment until research is done. But the stigma, as I said, is alive and well. Having a mental illness can make it impossible for you to adopt, for instance. Having a mental illness can place you at a severe disadvantage in a child custody case or, indeed, many other court cases. The mentally ill are still a scapegoat for everything from gun crime to white supremacist violence. We can be denied jobs, fired from jobs, and even lose our homes if the wrong people find out that we’re mentally ill. Unless you have a good economic cushion, options for assistance for the mentally ill are few and paltry, and the rest of us are likely to wind up on the streets or in the penal system without that assistance.
I think this contributes to the reasons those who want to garner sympathy and attention by claiming an illness choose a mental illness, in fact. Among some folk, there seems to be this weird “adversity envy” and for some of them, mental illness is an answer.
I couldn’t say how much of what any of it is, but these are the possibilities.