It sounds like we more or less agree then, in principle, on the government ownership side of things. However I do have a few minor quibbles (see below). It's also worth noting there are instances where the government pricing is inefficient because they are
not giving certain things away for free.
A concrete example (from Australia), although you might again accuse me of 'picking edge-cases': the Australian government charges between $20 to $40 for downloading information from the national corporate registry (e.g. per-corporation information about shareholders, directors, company address etc.). This 'product' is very obviously provided by an automated script pulling information from the corporate registry database and shoving it in to a PDF template. In other words, the marginal cost of production is some number approaching zero and there's no argument for price-rationing given consumption is almost perfectly non-rivalrous. In effect, the government is levying a very narrowly based sales tax at a rate approaching infinity per cent. Not particularly efficient.
That aside, and more on your example (roads): I agree that road-usage is mis-priced by the government and it would be economically efficient to levy a 'variable congestion charge' (like Singapore, as you note). This would also naturally put a brake (heh) on government over-provision of road infrastructure. However, and this is what led the government into trouble in the previous example, when setting the price for using the road, the government's objective should not be profit maximisation. Rather, the government's objective should be maximisation of total social welfare (total social benefit - total social cost). In your specific example (roads) it's a near-certainty that the profit maximising price (i.e. private market price) and social welfare maximising price are very different, as roads tend to be natural monopolies.
So I'd suggest the phrase 'market price' in this context is probably not the best one to use: if public roads were privatised, the 'market-price' would be the 'monopolist profit-maximising price'. This produces a socially sub-optimal outcome as well as an economically inefficient one (i.e. monopoly pricing results in deadweight loss, except in the extremely unlikely edge-case of perfect price discrimination).
Lastly, it's pretty disingenuous for you to say I'm just picking out 'edge-cases'. Yes, you're correct that water is abundant at the moment (and therefore has a low market price). And yes, sometimes acts of charity by the rich (which are commendable) can alleviate minor equity concerns or correct minor market failures. But if you'd like me to choose something you might consider a 'non-edge case', I'm willing to give it the old college try:
It is estimated (conservatively) that 13% of the world's population suffer from undernourishment, and 9.6 per cent live in 'absolute poverty' (again using a conservative estimate i.e. the World Banks'). Reductions in global mal-nutrition and absolute poverty have been achieved, in part, due to massive government expenditures on overseas development aid (ODA), estimated at $160 billion in 2013 by the OECD. Private charities contributed an additional 15-20 per cent on top of this figure.
Even in the United States (a country noted for its culture of private philanthropy), it is estimated that roughly 1 in 4 children live in a state of 'food-insecurity'. It should be pretty obvious that (relatively minor) 'private charity' expenditures are hilariously inadequate for solving huge (and ongoing) equity problems like 'global hunger'.
So you'll have to pardon me when I say: your assertion that private charity can deal with 'edge-case' inequities and market failures is utterly insane.