Collecting taxes and providing, by hiring a private company, a service
vs.
Mandating that I purchase a private company's services myself.
In the first case, the government uses its bargaining power (all that money) to negotiate a lower price by requesting bids and selecting a provider. In the second case, I'm a captive customer with little, if any, bargaining power. My bargaining power does indeed depend on how this second arrangement is legislated and how many providers are available to me.