New York’s woke mental health system — which refuses to lock up even violent maniacs — is as much to blame for the unprovoked fatal shoving of a retired teacher as the suspect himself, critics told The Post. “It was the quintessential preventable tragedy,” Carolyn D. Gorman, a fellow at the Manhattan Institute, said Saturday. “I think there are two issues: There’s a lack of [patient] beds, and there’s a lack of willingness to hold individuals, whether in a locked psychiatric facility … or in a locked jail or prison. “We have to hold these individuals somewhere. … But if we are not willing to hold them somewhere where they can receive oversight — whether or not they’re receiving treatment at some point — it is a danger not only to the individuals, but to other New Yorkers.” Rhamell Burke, 32, allegedly shoved 76-year-old Ross Falzone to his death down Manhattan subway steps in an unprovoked attack Thursday night.…