If government were operating on a profit motive it wouldn't be doing the things it should be doing.

Government should focus on exactly those things where a profit motive doesn't make sense, i.e. areas where maximising total well-being does not correlate with the ability to extract a profit.

EDIT: So efficiency as applied to government services should really be based on very different criteria than profitability. Though to a lesser extent that is also the case for private companies.