My experience is the opposite. Private companies seem completely inefficient compared to government, and I've worked as engineers in both.
Really it is only a right-wing profit-driven talking point to say government is inefficient, mostly to protect against their profits that government takes away.
The numbers support my case. You can send a mail with the USPS for 50 cents anywhere in the country, but it costs $5-$10 to do the same with UPS or FedEx.
Literally 10x-20x costlier.
Government just doesn't have to waste money on things like profit or marketing that private companies need to do.