There is no contradiction between "show me the money" and "ethics and integrity".
It's even sillier than that
"some of them will see what is being done to them"
Don't you feel guilty about abusing the english language this way, by using passive voice to insinuate an affirmative harmful action by someone? And yet, in reality, all we're talking about is resistance to being made to give our stuff to someone else. It's not a harmful action - it's at the very most neglectful inaction, and even that only if you presume some sort of inherent moral claim on other people's labours.
The mechanics are lovely, but it's funny to define "complete life cycle" their way, as though death/destruction were an interesting or difficult achievement of life (or machine operation).
If the likelihood of a positive return was high, people would undertake personal debts for it.
"in general pay for themselves"
Note that even this happy-hypothetical-scenario is all from the point of view of the government treasury. From the point of view of individual net-taxpayers, there is no pretence of "return" on their "investment".
"We're supposed to use the government to oversee the process
and keep it honest, make sure contracts are completed."
That's what the courts (contract/tort law) are for - a Department of Roadbuilding is not needed for that.
"government handouts are the best way to distribute a good. See justice, fire protection and military defense for undisputed options"
Note that not one of your examples is actually a government "handout of a good". They are services provided generally, not as transfers to specific individuals.
... then that one in a thousand will help subsidize the 999 until the money runs out
It hasn't run out quite yet.
(Sorry, but "the right" in context means conservative type people, not those states that happen to vote republicans. Equivocating the two is a category error.)
The right doesn't "want stuff" taken from other people. They want to earn it.
"bankruptcy is not normally on the table for nations"
It's a funny-shaped table then - even the US has gone bankrupt a few times, e.g. when reneging on their gold-convertibility obligations.
That "infographic" proves the matter - disregard its absence of info.
... too bad that catastrophic-only coverage has been made apprx. illegal by obamacare.