One of the most common vehicles for this are Sovereign Wealth Funds: https://en.wikipedia.org/wiki/Sovereign_wealth_fund

Norway uses one for their pension program (AUM of > $1 trillion, owning over 1.4% of the global stock market, https://en.wikipedia.org/wiki/Government_Pension_Fund_of_Nor...)

My favorite one, however, was created by Ronald Reagan, the United States Mint Commemorative Coin Program:

> Since the modern commemorative coin program began in 1982, the United States Mint has raised more than $506,301,189 in surcharges to help build new museums, maintain national monuments... and much more.

https://www.usmint.gov/news/inside-the-mint/commemorative-co...

Honestly a world where the government has, say a commercial for-profit version of NPR, high speed internet, etc, that coexists with other current offerings and then re-invests that into government programs and needs less tax dollars from me sounds like a great idea. Tax payer money already paid for most of the infrastructure, we might as well profit from it.

There's some odd political animosity to it however, as if asking for a tax-payer owned version of NBC with some entertaining primetime shows is like some kind of slippery slope to autocratic socialism ... it's actually bringing capitalism into the government like never before and allowing them to say, not have to ask me to vote on raising my sales tax to build a train. Instead they ask us how we want to use all those sweet profits.

... it'd be nice ...

Lots of government operations around the world make a profit. Usually the money is reinvested to improve operations, but it can also be sent back for general spending depending on the structure of the organisation. Now, it's been a very long time since I lived in Canada, but the Liquor Control Board of Ontario (LCBO) used to make a tidy profit. It also used to be the largest single purchaser of wine in the world and as such was able to get incredibly rare wine. Back in the day, if you wanted to tour a winery someday, you could often set it up with the LCBO and the winery would absolutely roll out the red carpet for you. Not sure if that hack still exists, but it was pretty sweet 10-20 years ago. Although unpopular with a lot of people due to all the politics that a government monopoly on alcohol gave, the LCBO was profitable and provided surprisingly good value (as long as you happened to live near a store where influential people lived :-P ). Like I said, it's been ages since I lived there, so I'm not sure what the current status is, but it lasted a long time due to its ability to deliver service and provide revenue for the government.

Antrix Corp owned by the Indian government provides satellite launch services. It made $31m profit on $210m revenue in 2017-2018.[1]

1. https://en.wikipedia.org/wiki/Antrix_Corporation