1) Government libraries should be privatized by incorporating each of them and distributing the shares among the residents (ideally, the landowners) of the neighborhood/community it serves. If local landowners agree that the library's contribution to their property values is worth its operating costs beyond its usual fees and donations, they can vote to be assessed an ad valorem tax on their land, which re-captures the value the library allegedly adds. If a library is not-for-profit and open to the public, then it would be exempt from the land-value taxes that finance most of government in Libertopia.
2) Along the same lines as government libraries, each government park should be privatized by distributing shares to the residents/landowners of the area it serves. Conservation groups could buy up shares of parks they are especially interested in preserving. Not-for-profit parks open to the public would be exempt from land value taxes. Government land that is not already serving as a park should be opened up for homesteading, with homesteaders bidding for leaseholds and subsequently paying a land value tax based on their lease. If someone offers them more than their current basis for their land-value tax, they either have to sell or raise their land-value tax basis to match the offer. This of course is the general model of land-value taxation in Libertopia.
3) Pollution is aggression, and should be policed at the most-local practical level of government with Pigovian taxes. Also, depletion of a natural commons -- oil, minerals, wildlife, aquifers, streams, lakes -- should require a fee paid to the most local level of government that represents the people most impacted by the depletion.
4) There would be no such advantage for wealthy corporations as long as 1) existing assets are distributed as shares to the members of the relevant community and 2) the natural commons is protected with taxes on pollution, depletion, and site monopolization. (Taxing "site monopolization" means a land-value tax.)
5) Artificial monopolies, e.g. on oil, are not sustainable and never last. Natural monopolies -- on physical networks like streets, pipes, and wires -- should indeed be regulated by local associations of the landholders that those monopolies serve. The distinction between "government" and homeowners' associations will then be -- and indeed should be -- quite blurry.
6) According to the geoist analysis, much of existing inequality stems from 1) appropriation/pollution/depletion of the natural commons without adequate compensation to those whose access rights are thus impaired, and 2) labor being taxed to fund public goods/services that increase the value of land which is mostly owned by non-laborers. Depending on how the transition is done, the standard anarcholibertarian scenario would indeed very likely bless and exacerbate these two kinds of inequality. By contrast, the geolibertarian policies described above are designed expressly to restore everyone's equal liberty and equal right of access to the natural commons.
For more on geolibertarianism, see http://earthfreedom.net/.