You, the professor and I agree about Gautrain - it doesn't meet the criteria of a mass public transport system - accessible to and used by large numbers of users, relatively cheap cf other forms of transport, etc.
I've never used Uber but UberX is about R7.50/km Jo'burg (CT R7), below metered taxis but above minibus rates. Uber is NOT mass transport - your (and Ivo's) definition of mass public transport is way off.
About public goods, one would think taxpayers and governments would gladly pay for it but like most items we have alternatives for, eg private transport that has numerous benefits over public, it's a grudge expense. Would we object to, say, expensive desalination plants w/ climate change (that Ivo disputes) upon us causing long-term drought and dams empty? (Well, ok, we might.) But how come SA fell over themselves to host World Cup 2010 costing $4bn at the time for almost no economic benefit? Ivo, where do you stand on that?