I agree with you that the triumvirate of Stuy, Bronx Science and Brooklyn Tech are not the best options for all high performing students. They are heavily math and science oriented and known pressure-cookers. In retrospect, I would have gone to Brooklyn Latin or Bard or Beacon in my day if they were options. Instead, I went to Stuyvesant. It was that or Brooklyn Tech, and my JHS teacher’s said I should go for Stuyvesant. 
Regarding Bard’s assessment test. Is it graded? Are the results public? I imagine it’s one of many criteria and the admissions team exercises it’s own discretion. Much like Harvard exercises discretion. I don’t think these schools are pure meritocracies (if meritocracy measures grades and standardized test scores). I also gather Bard is much more diverse than many of the SHSAT schools. It’s about 39% white, 24% Asian and about 33% African-American and Hispanic. I think very talented African-American and Hispanic kids at Bard, in another era would probably be at Stuy or Brooklyn Tech.
I agree the diversity of programs are wonderful and very exciting.
I think there are more options for students these days, which may, indeed, be contributing to the decrease in White, African American and Hispanic presence in the SHS,
I do think, however, that the DeBlasio and Carranza are unfairly targeting the Asian community just because they found their niche - the SHSAT dependent schools. They aren’t targeting Bard, Beacon and the like, even though they are not representative of the overall demographic of NYC public schools and are much more favorable to White students. The optics of the demographics at schools like Bard and Beacon aren’t nearly as egregious as what we’re seeing at Stuyvesant, Bronx Science or Brooklyn Tech, but, if 15% of the public school population in NYC is white, and some of these public country day schools are over 50% white, and the criteria isn’t one objective test, you would think there might be some red flags going up here.
I’m grateful that schools like Bard and Beacon are providing an excellent education to diverse students. However,
It’s a lot harder for DeBlasio and Carranza to go after the white power base than it is to go after the Asians. And as our Asian friends are pointing out, "Why are you mad at us just because we are passing one objective test and neglecting the interview based schools with much more subjective criteria that are still favoring whites at three times their representation in the population?