The problem with this is people investing their time/expertise/money/energy into the common good and then have a small number of people ruining the benefit for their own ends, knocks the well-meaning out of the most positive people. The common good only works well when everyone wants the common good.
You seem to have independently discovered the market failure commonly know as the Free-rider problem, for which there are many solutions, and which is not a dispositive preemptive argument against the establishment or management of common good(s).
For example, Elinor Ostrom won a Nobel Prize for her work illuminating design principles illustrated by long enduring common pool resource institutions.
> Ah, then my second wish will be for everyone to want the common good.
People have very different, often contradictory opinions what the "common good" is.
I would even claim that this question is a special case of the millennia-old philosophical problem of defining what "good" actually means (i.e. defining ethics), which has resulted in myriads of different opinions: