Can the existence of public goods be a source of market failure?

Its not the existence of public goods that leads to teh market failure it is the need for their existence that is the problem. In other words your local state school isnt a market failure the need for its existence due to the underprovision of the private sector is what is the market failure.
Yea but only one! A small one at that. There are literally hundreds sources for market failure. Public goods are just one of them, and that has to work in conjuction of all the major reasons, combined with the minor sources. It's not just one aspect that will do it.
The percentage of goods considered public is in inverse proportion to the success of the market. The greater the public ownership, the lousier the market. See, for example, the economic history of any nation which suffered through Communism.
Yes, maeket mechanism does not lead to efficient allocation of resourses or maximisation of social welfare. But this can be corrected through approriate adjustments to market mechanism in respect of the public goods. machanism to some extent. Unfortunately, so far no body has invented a non-market mechanism that would mamise social welfare in the absence of market system. This is a petty that such non-market mechanism human talents are a total failure.
Public goods is only one case of market failure. There are two other conditions of market failure. In contrast non-market mechanisms are purely ad hoc and fails in every sohere and field. Surprisingly, those who fail to compete in market system themselves are unable to accept their inability to invent a non-market mechanism that is efficient and delivers maximum socual welfare, unless one assumes that only their wishes are the best indicators of social welfare.

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