If the governmental body is not interested in ensuring efficiency, than no matter what structure is chosen it will be abused - by inflating counts, or costs, or some other way, because people who have incentive to get money and no counter-incentive to follow the rules will cheat. Not all of them - but enough of them to cause serious damage. Look what happened in California recently - about 27% (!!!) of unemployment benefits is now thought to be fraudulent. This is what happens when people are incentivized to cheat and people who oversee the public coffers aren't incentivized to guard them. You'd expect that there would be some consequences for CDC leadership for their numerous failures - but that's not happening.

There are systems like that within the government, but in those scenarios the Contractor owns the system and deploys it as a service. While it can be cost effective in the early years, it does entrench the Contractor and make it difficult for the Government to switch because they own nothing.