From a security point of view, the question is not whether the inputs are random, it is whether they are vulnerable to manipulation. Having more inputs does not make a system more robust against this type of attack, it makes it more vulnerable.
If we are changing our ECC curves due to the possibility that NIST might have been suborned, we should not be using a number so obviously capable of being manipulated as an input.
The reason that we can trust lottery numbers is not that they are absolutely immune from tampering. We can trust them because anyone who could be bothered to tamper with them has a much bigger incentive than manipulating the IETF NOMCON choices. This means that we can put a dollar value on the manipulation, a few hundred million USD.
The issue isn't just whether an attack is likely, it is a matter of reputation. We are not changing our curves because we believe NIST manipulated them. We are changing our curves because some Major desperate to make Colonel and keep their job wrote a bunch of silly slides that leaked. And given that the agency concerned has an up-or-out promotion policy and the person in charge only values attack as a strategy, the slides were all designed to present the work done as attacking and manipulating.
[As an aside, expecting people who work in fear of their jobs to take courageous acts against their commanding officer when ordered to commit illegal or immoral acts is naive at best.]
I suggest we remove the US debt from the equation entirely as it is not an appropriate source of randomness. The internal means of construction is not opaque, nor is it automatic. Ergodicity is not the test that matters, transparency is.