That wasn't my argument at all.
My argument was pointing out the common problems with a bid based approach. In almost every locale, bid-based contracts are a bigger source of government spending waste than inflated government employee salaries!
For something as generic as a law enforcement job or civil servant job, I don't see the potential for the problems you mention.
Instead of two or three contractors and a murky selection process subject to under-the-table payments, you have a large selection of very similar candidates, and the selection process is as simple as "how much will you be willing to do job X for" with the low bid winning.
Somewhere, some economist professor has to have named and analyzed this type approach.