To build a development you need planning permission. This will often include an agreement that public open space will be provided as an amenity for the community. Sometimes this will be as mitigation for loss of other space. Or just as a something the local authority wants. It is probably better than stricly gated communities that exclude the public community, which is what the councils want to avoid.

Also, the council may not have the funds to properly maintain the open space if it was handed to them. It makes commercial sense for operators to do landscape work themselves if that is something that matters to them. People want retail, housing developments or high end office blocks to be attractive and well maintained.

In New York they get valuable zoning concessions.

It's explicitly transactional, in consideration for the property owner providing and maintaining the space, they get to build XYZ. And as the spaces are typically adjacent to their properties, they are motivated to keep them well maintained.

The alternative seems to be that the developer build smaller, or not build at all, and provide not public space.

I would imagine as well it is sometimes (in the UK at least) part of the planning consent from the local council to provide these spaces.

Public relations and advertising. They give that land to public use, after all, so that everyone can enjoy it. They support parks. And so on.

real estate / land value