This article suggests that Summit cost somewhere in the low $100 million range and last I heard from DoE that was accurate, so they aren't exactly paying retail.
Price isn't really a concern with these computers, though, because the sort of experimental work they are intended to "replace" (using that loosely, since a lot of the things they simulate are impossible to actually do) is far more expensive. Leadership-grade computing is all about enabling new classes of problems to be solved.
Regardless of the leadership position, most of the time a bunch of money can be allocated from nuke maintenance budgets. Maintaining a massive nuclear arsenal without testing requires a ton of computing power and the cost of upgrading supercomputers a few times a decade is a rounding error.
Summit is an open science machine (meaning any researcher can apply for time, but it's very competitive so getting an allocation is difficult) and is not budgeted to NNSA for stockpile maintenance as far as I know. It should be running mostly non-classified scientific research, though there is a provision for running sensitive research like stuff related to operating nuclear plants. Sierra at LLNL is the one that is primarily targeted towards classified weapons-related research and NNSA operates independently within DoE.
It's not budgeted for it but I heard that some of the FastForward 2 program money ended up going to ORNL because NNSA needed to do some early stage verification that was prohibitively expensive for them to do on their own but trivial for Summit (since they were already getting the hardware).
AFAIK there isn't a single publicly owned supercomputer in the US that wasn't funded in small part by stockpile maintenance budgets, even if they were never used for that purpose.
Very likely true. I know that stockpile maintenance is at least a tangential concern for all of them, even if it's just to have something available in reserve. Budget allocations are complex beasties, especially in DoE which pursues a variety of missions. The vast majority of work on the ORNL computers is not weapons-related, however.
I don't know for sure obviously, but based on my time in the semiconductor industry they will force lower volume sales through distribution (even if the part is not generally available). This is for financial risk and supply chain reasons (e.g. RMAs, shipping/customs/tax/duty).
Nvidia was probably under contract for this before mining blew up to where it is today. Provisioning for these machines starts 5-10 years before they ever come online.
