doesn't the trend to outsourcing many governmental services makes governments simpler?

The government has to outsource in a governmenty way. So in the US, they're not allowed to unfairly favor one company over another (at least there are rules trying to prevent it). This makes the steak and strippers kind of selling illegal, and employees of contracting companies are legally required to go through training on how not to bribe officials. Companies have to re-compete for contracts they've already won. Then you have subcontracting, which leads to situations where your boss works for a different company than you and isn't allowed to know your salary.

Maybe it makes things simpler for the government itself, but probably not to the extent that it could.