When I do incident command at my workplace, there are two goals in dealing with an incident: solving the problem, and preventing it from happening again. They are both extremely important, but they happen in order.
While the incident is ongoing, any attempts to prevent the problem from happening in the future are a complete distraction. Write down notes and ideas somewhere so we don't forget, but the priority is on solving the incident that actually happened and is causing problems. If you say "What if we fixed this longstanding piece of tech debt that led up to the incident," however reasonable it is to fix it in light of the fact that it caused an incident, it's useless to bring it up now if you can't fix the tech debt immediately to resolve the incident. Along the same lines, attribution is interesting if it will help you deal with what is going on (e.g., there's high load on a low-level system and you want to know if anyone deployed anything recently, so that you can ask them to roll back); it's not really interesting if you know what's broken (e.g., a machine is powered off and needs to be turned back on... figuring out who pressed the power button isn't yet relevant).
Similarly, "We should stop funding gain-of-function research" may (or may not) be a valid conclusion, but it wouldn't have dealt with COVID-19 in particular. It might be worth doing it to make sure there's no COVID-22.
Even if it turns out to be true that COVID-19 came directly from research that would not have happened if it were not for Fauci, absent a reason to believe that anyone's response to COVID-19 specifically would have been different if they knew that, I don't see any reason it was improper not to draw attention to it at the time, and quite a few reasons why it was proper to focus attention on the problem at hand.
His comments in that May 2020 article are spot-on. If we knew that it was engineered, then yes, publicizing the lab notes that were used to build it could perhaps speed up the process of a vaccine or other countermeasure (but COVID-19 had already been sequenced by January 2020 and the sequence published, and vaccines were already in development then). But theories like "what if the researchers brought it in from the wild, and then it escaped their lab" should just have prompted the response "yes, so what." It's interesting now to prevent the next COVID; it's irrelevant re COVID-19.
And I certainly don't see the conflict of interest - what was Fauci gaining? His continued role? Again, at the time, the role was not determining whether to fund gain-of-function research, the role was figuring out how to get rid of COVID-19.
You could say that the NIH should have paused all funding for new virus research projects (unless they specifically related to dealing with COVID-19 in the short term), but that would have been a good idea regardless of the NIH's previous role in funding.