There's a question of motivation.

A public service ought to be motivated to deliver a good service. It won't be motivated by taking shortcuts. A private company seeks profit and cannot afford to lose money, contrary to a public service which can be not profitable. Offering a good service it a means to be profitable but that's not the end goal, even if many people actually want to do good work.

Of course there's a big if. IF the government throws enough money at it.

This IF is unfortunately too often "IF only". If not, we are back to shortcuts.

The service I get from AAA's DMV services is far superior to the service I get from the DMV itself.

bureaucrats and civil servants get paid regardless of how shit they do their jobs because the government puts a gun to your head to pay their wages and consume whatever service they provide (also applies to some "private" companies)