It's my fault to have brought up the term "veil". To expand where I'm coming from: I think that they even talk about it in the context of energy research is a veil, cause I don't see any way how this will ever be used for it. IMHO, it's only useful for weapons research. But maybe it's just a lack of fantasy on my part and it is possible (in a useful way, not possible in a "we could do this, but it's so blatantly stupid, why would anyone ever think we'd do it?" way).
I know essentially nothing about the field. I can imagine how it might be used to understand how plasma works, and how to measure plasma activity, specifically in the domain appropriate for fusion reaction instead of thermonuclear weapons, might be relevant.
I conjecture this because I read about how knowledge from thermonuclear weapons development helped inform our understanding about how fusion works in stars, even though the experiments themselves were secret.
The story was of a Soviet astrophysicist visiting the US. He gave a lecture about stellar processes. A US grad student asked him afterward about one step in the process, something like "how do you know the plasma is transparent to X-rays?". The Soviet scientist said simply "it is." The US student, confused about it, asked his US advisor, who informed the student that it meant the Soviets figured it out as part of research for H-bomb development. I don't have a primary source for it though.
As a possible parallel, Shepard's suborbital flight used a Redstone ballistic missile, modified to make it human rated. Space flight and space telescopes are closely intertwined with missile technology and espionage/surveillance.
Here's a NYTimes article about six companies attempting laser fusion for power production. At least two have personnel from NIF. One uses an approach similar to NIF's but with modern lasers, and a couple others use a different type of laser that removes the need for the hohlraum.
Also it says "A decade ago, a report by the National Academy of Sciences found much to like in the energy potential of laser fusion but recommended that the United States hold off major investments until ignition was achieved. That time is now." Here is the NAS report:
https://www.ans.org/news/article-5611/three-new-inertial-fus...