"The optimal amount of fraud is non-zero."
No, the optimal amount of fraud is ZERO.
The cost of fraud detection and prevention is different, but in an ideal society, the taxpayers aren't paying for fraud (because the people don't scam the government).
If fraud detection is so expensive, maybe it's important to be more selective of who has access to the community and keep the scammers out.
And how would you "be more selective" and "keep scammers out" without incurring more costs? At some point, it costs way more to prevent the last 0.1% or 0.001% of fraud than would be saved by preventing said fraud. And the cost might be paid by non-fraud being detected as false positive.
Your salary was the exact kind of thing that needs to be balanced against the cost of fraud; if it was larger than the amount of fraud you prevented, then the company would have been better off just accepting the fraud as a cost of doing business. The closer you get to zero fraud, the more expensive it becomes to reduce it further (and the more likely your countermeasures will negatively impact the business in other ways), so there definitely is an "optimal" balance to be struck between fraud and preventive measures.
You don't live in an optimal world so what use is it talking about? Are you also doing your business calculations using frictionless spherical cows in a vacuum?
Simply put every living system on the planet earth has some amount of parasites. To have no parasites at all would require massive amounts of energy by the host to ensure said parasites don't exist. If the host can spend a much smaller amount of energy and ensure that 99% of parasites don't exist that is optimal thereby negating your original premise.
If fraud detection is so expensive, maybe it's important to be more selective of who has access to the community and keep the scammers out.