That may not be a bad idea, even if you are doing the same work twice. A project that Google or Apple would spend $100M on could pay $75M to the loser and $130M to the winner and still come out better than the current system.
However, to make it worth doing for $150M, you'd need to seriously reduce the government paperwork and delays, the layers of approvals for little minor stuff. Where I work, a government agency, the budget specificity is maddening. The state approves $X million for new computers, I had to spend $4,800 on a new workstation even though the old one has 16GB of RAM, four monitors, etc. A few months later, my UPS battery went bad and needed a $25 replacement. It's been weeks and I'm still waiting for approval to replace the battery.
My colleague saved $30,000 on a project by pointing out we had already purchased the thing we were supposed to spend $30,000 on. This is a big problem, trying to figure out how to send that $30,000 to /dev/null. We can't spend it on things we need, like batteries, because it's not approved for that use.