That happens all the time in the public sector, with e.g. lucrative contracts being supposedly offered for anyone who can fill the requirements and bids the lowest, but with the requirements being intentionally crafted so that only a few favored organizations can match them. Without such a setup, other organizations might actually get their offers into consideration.

If someone is corrupted enough to design the requirements so that they match a favored organization... what will happen if the same person is allowed to make the same decision, without the condition of choosing the lowest price? I guess the same favored organization will get the contract, only the price will be much higher.

(Case study: This is how highways are built in Slovakia from European Union's PPP money. When one specific political party is in government, only 20 kms per year are built for the same money that was enough to build 100 kms per other years. The reason is that all contracts go to companies belonging to the boss of the given party. All competing companies are refused, officially because their prices are "suspiciously low".)