If society benefits from a good or service, but there's no profit to be made providing it, why shouldn't the government provide it instead?

They should and they do. Fire and Police Departments and our military, Consumer protections, regulations against polluting and poisons, etc. Thats what government is, thats the reason for it.

I prefer that governments stay within their charters or constitutions.  

And if the charter or constitution needs to be amended, that it follow the designated process to amend it.

The trade-off here is that a good or service may be beneficial to society unless and until it is provided, and thus controlled, by government.

The reason the authors and ratifiers of the US Constitution put limits on the federal government is because human history was replete with governments which abused their powers and their citizens, with very few exceptions.

A good or service that benefits society has value.  People are willing to pay for things of value.  Government is the least efficient source of anything.

"GOVERNMENT MONEY" DOES NOT EXIST!

It's TAXPAYER'S MONEY.

If one person gets something for FREE it's because the Govt STOLE the money to pay for it from working taxpayers.

Absolutely.....or even if there is a minimal profit, which could go to reducing taxation

I would need some examples to answer.

I didn't really think you had any examples. But let me help you. Charities would fall under your criteria. And we have many private charities. When government is involved in things like charities corruption tends to grow. Especially when it is charity to foreign governments.