The posted answer:
Absolutely, that's why cities are mandating them and have been mandating them for a couple of decades in Texas. The city of Garland has representatives testifying to that effect before the Texas State Legislature the last several sessions. This is a disease that has been spreading for a while. The city/county comes up with some "public benefit" that will be mandated for the property (open area, water retention, etc.) and then mandates a private method for taking care of it. Even in areas where the HOA has become defunct, the cities/counties are suing to force creation/revival of an HOA to assume those public responsibilities.
Not only does it eliminate the cost of maintaining those areas, it also ensures that the so-called common areas are privately owned and therefore subject to taxation. If the city/county owned them those areas would be exempt from the tax roles. Instead the city/county is mandating these areas in subdivisions but they are privately owned. This means they will be on the tax roles and privately maintained at the expense of the homeowners in that subdivision. The HOA owns the common area, not the homeowners.