Pretty much, yes. Broadly speaking, the US federal government's financial controls are good and prevent a ton of corruption and waste. At this scale no system can be perfect though, and there will always be some.
However, there are diminishing returns at some point. If you want to go after, let's say, the 99th percentile within which things like soap dispensers might fall, you may have to spend more in admin costs than you get back in savings.
This applies to both needing more staff and needing to add more paperwork, which also in turn can slow down projects.
This DoD IG report, for instance, faults the US Air Force for not having built a database that tracked historical prices and tracked equivalent COTS part prices on various commercial marketplaces. That means either having staff or (more usually) paying some third party contractor to maintain a database and constantly update it to track all of these commercially available products. At some level you can end up spending more than you save.
That's why in corporate audits there's always a threshold floor below which external auditors don't bother to check further. It's considered an acceptable risk.
With regard to historical pricing, I agree. I suspect that's more an admin oversight than the lack of a system though. But in terms of the equivalent product price comparison database, would that really normally be in place? I would think the space of aircraft parts that could potentially be replaced with COTS parts is not a very large one, and probably not something optimised for at first. Instead, focus would first be on tracking/monitoring military parts, then of separately tracking clearly COTS parts.
Also, there's a human aspect here. Doubt any air force officer wants to be the one to approve a COTS replacement for something like this only to have something go wrong on a flight because of some or other unexpected failure.
