National Infrastructure Bank

All of today I've been trying to wrap my head around why a national infrastructure bank would be a good idea. 

After hours of googling, reading, and talking to myself - it just seems like it has a lot of potential to be good for the people but the proposals that are out there are not headed in that direction.

The whole point of a NIB is to increase infrastructure investment.  Though there are many proposals they all have this sort of structure:

A NIB is originally capitalized by federal fund appropriation - the government says its okay to start a bank and gives it $x amount of dollars- lets say $60 billion- to start with.

They can use that initial starting money to "leverage private investment" which I think means use some sort of mechanism to make the $60 billion into $120 billion (maybe through a bond offering or something). But they don't have to do this, they can just stay unleveraged and stick with the $60 billion.

They take applications for infrastructure projects that state/local governments or private firms would like to do and pick the best ones and give them low-interest loans.  The projects usually have to have some sort of monetary benefit so the loans can be repaid- like taxes or tolls. 

Upon repayment, the NIB can make more loans. 

The increased infrastructure investment comes from the fact that these borrowers probably wouldn't have made these investments without the low-cost loans. 

This seems to make sense.  However I have questions:

First- is it actually the case that state/local governments and private firms are credit constrained? Maybe they actually have access to loans that aren't high interest but they just don't want to make those investments. 

Second- how is this sustainable? Banks offer low-interest loans to finance these projects and owe interest to bondholders - is the spread really that big?

Third- the only thing that the NIB seems to be incentivizing is projects that have future revenue streams like tolls and taxes. This is what makes them want to offer the loan in the first place.  However, does this mean the only infrastructure that is being increased is infrastructure that will further tax people.  Aren't the federal funds used for initial capitalization our tax money already? We are being taxed to fund further taxation.

Fourth- the projects that have the most social benefits are exactly the ones that can't be charged per user.  It is easy to imagine Amtrak wanting a low-cost loan from NIB to expand their services but why the hell would anyone want to take out a loan to improve a public good?

To be fair I did read something about California's I-bank doing some good stuff - like making sure communities benefit from these infrastructure projects and that any wages paid via their loans are good wages.  This type of leveraging I'm down with.  

The NIB will probably increase infrastructure spending but also

enrich bondholders
not be sustainable
tax on tax on tax
give companies low cost loans to charge more fees

Wouldn't it be easier to just tell the government own up to the responsibility for our infrastructure?