The Sanitation Department is committed to recycling, and the DOT to biking only to the degree that those agencies are directed to be so by the Mayor. If we want the City to reorient its priorities, it's to the elected officials we have to address our concerns.
I agree that if the Mayor orders them to do something, they would snap to attention and get it done. However, there is a great deal of everyday discretion that agency commissioners and deputy commissioners have over how to deploy their resources.

I feel the evidence of the city council setting up an independent recycling in the CENYC is proof that some elected officials did not believe that the current DOS would follow their directives to increase recycling.

It's a two way street. The Mayor should give strong direction to agency commissioners. At the same time, I would hope that agency commissioners are not just doers, but also thinkers, who put forth innovative ideas to the mayor, the city council and challenge their own staff to excel in all their responsibilities. That's what real leaders do.