The US contracted with a company to train Afghan army intelligence, in 2010-2013. That company failed completely to do the job; then it massively cheated the US government, but the officials weren't bothering to check and it took them almost a year to stop paying false bills.

If someone tells you that the private sector works more efficiently, remember this example.

The company failed to keep complete records to justify its supposed work, and so did the subcontractor it hired to actually do the work. Meanwhile, I am sure two levels of private business, each of which had to tack on a profit, increased the cost substantially. That is what privatization of a government service typically does: it costs the public more, skimps on doing the job, and usually pays employees less, "because we have to make a profit".