My reason for saying that States should handle Medicaid is because a huge bloated Federal bureaucracy is incapable of policing itself.
A State, being smaller, has a better chance to discover fraud and abuse, keep costs down, then correct its own program. Why? Because voters are closer to the problem in a State and can have a huge impact on State programs via the ballot box. Not so much with Federal programs.
I would wager that 40% number would come down if there weren't stupid and wasteful Federal regulations involved.