While the 3rd scenario does sound good on paper, in reality it is not. The fact is that government is worse at spending money then the private sector is (in other words it is spent less efficiently). You imply that the government would pay for all this which means that taxpayer money would not be spent efficiently (all money that government spends will eventually be paid for by taxpayers), unless you are part of the 47% who pay no taxes and rely exclusively on government you should care about this. For example the 2009 stimulus package that president Obama and the democrats passed ended up costing around $300,000 per ~$40,000 per year job created as a result of the stimulus.
I haven't read the discussion from the beginning it seems. Because this premise is wrong in the modern monetary system:
all money that government spends will eventually be paid for by taxpayers
Another problem is that you assume that we need more/better infrastructure. In many cases we do not and the money would be spent on things that would not even be used. One example of this is the $100 billion bullet train to no where in CA. Not only is the project expected to generate vastly less amounts of revenue then it will cost to build, but it is estimated to be greatly underutilized.
There's always something to improve. If infrastructure is perfect, then spend money on fundamental science, medicine, education, whatever.
All money that government spends does eventually need to be paid for by taxpayers. Even if the government never pays back the debt they incur to spend this money the government will need to have otherwise higher taxes in order to service the debt forever.
All of you suggestions for government to spend money on other things (science, medicine, education, ect) could be more efficiently done in the private sector.