Sure, but to go back to my analogy, you absolutely do put the guy who hit the power button by mistake in charge of pressing it again - they know exactly where it is and they're already in the datacenter. You put the team that deployed a new service that's DoSing your infrastructure in charge of rolling it back. You don't say "You broke the system, so we're finding someone else to do the rollback."
If the allegation is that Fauci intentionally funded a lab in Wuhan to work on gain-of-function research with the express purpose of having the virus escape and cause a global pandemic because Fauci is a murderer rivaling Hitler, that's a very different (and much harder to substantiate) claim than that he merely was causally involved in an accident and like anyone else wants the accident to not have happened.
And if that is the claim, the "conflict of interest" argument becomes clearer: Fauci is on the side of COVID-19 and in charge of stopping it. It's the same conflict of interest as putting an arsonist in charge of fighting fires.
Short of that, the idea that he had a conflict of interest is like the idea that the team that accidentally DoS'd the infrastructure has a conflict of interest because they each get Fauci-scale salaries and they might be fired. Technically yes, but we all know that firing them wouldn't help solve the problem and losing their expertise would make other things work, so it's not even on the table unless we suspect malice is involved.
(And if it is on the table, either at my workplace or in Fauci's case, so is criminal prosecution. Loss of salary is the least of your worries.)
You make comparison to tech workers. Sure, if someone makes a genuine honest mistake then you can argue they should be retained as they won't make that mistake again. But that does require deep and total honesty. If a tech worker caused an outage and then manipulated management for a year to cover up their involvement, there would be no such leniency.