* * *
The problem with a government investing money is severalfold, from practical considerations of incentive structures and consequences of the investment, to economic considerations of what investment really is and means, as well as where the money itself is coming from.
1. Incentive structures:
Probably the biggest reason why the government investing money is a poor investment strategy is that governments do not own the money they are spending, and will not receive back any money that is earned. This is to say, that the bureacrat spending the "public money" draws a wage solely, and the cash did not come from his pocket; and any money returned from the investment also does not go into his pocket. Thus, whether he makes a good investment or a bad investment, there are no consequences to him personally — he cannot be fired, nor gain any profit from the investment, and thus no incentive to weigh all the options, do due diligence, and make an informed choice.
Just look at the Obama administration's $500m investment in some energy company. The only gain the administration received from that was political gain, some talking points, some press coverage. They had no idea if that investment would actually help the economy, they just wanted to help a political ally (green energy).
2. Economic considerations:
All investment done by private citizens is surplus wealth reinvested. This means that a multitude of minds are involved in looking into investments, putting money where they each think it would best be invested.
How many people were taxed to garner $500m? Probably something like 100,000 people or more. The ability of those 100k people to hear about new investments, to network, to hear of problems with existing investments, or to stumble into a good investment dwarfs any government body of 10 or so appointed people, no matter how expert they are. And they are each investing their own money and directly receiving the pain of loss or joy of gain depending on how well they invested, which recalls incentive structures.
And if each thinks the investment they put it into isn't doing well, they can pull it and move it elsewhere. While the Obama administration was tossing around hundreds of millions at a time (into a single company!) 100,000 investors would've invested in stocks, bonds, entire portfolios of companies, resulting into hundreds and thousands of companies receiving funds to further their productive action. Which would've prevented the total loss of the investment as in the Obama's green-energy case.
And who in the Obama administration got fired for losing $500m? No one. It's play money to them, because they didn't earn it:
3. Where the money came from:
The reason the Obama administration could spend $500m of other people's money is because of statements like, "wouldn't it be a good thing if...?" It could be "wouldn't it be a good thing if retirees had free medicine," or "wouldn't it be a good thing if everyone had free education" — and the problem with such statements is that they obscure the consequences of implementation. Wouldn't it be a good thing... for who? and from who? Because every act of the government is done at the cost of human man-hours of productivity, turned into a wage, and then confiscated. Wouldn't it be a good thing if we had renewable energy? Sure, but who will pay for it?
To tax someone's wage to invest in a company is akin to saying that their income and effort must be sacrificed to the whim of politicians and their political goals. This money was taken from people who individually could've put it to much better use.
If a company is a good investment, let the free market invest in it, where the actions of many, based on their own judgment, and to their own gain or detriment, will make a choice free of political considerations, ensuring that it will not be the politically connected that get funding but rather those actually being productive.
The main problem is centralization. When you take money from dozens or hundreds of thousands of people, you cannot invest it better than they could have. This creates natural inefficiencies. Smaller amounts of money invested in more companies with more eyes watching the outcome of the investment, tracking it, and with the incentive to make sure it does well will always outperform a fiat decision by government.
I suggest Thomas Sowell's Knowledge and Decisions for a closeup look at the inefficiencies between centralized decision-making and decentralized decision-making and why that means communism and it's variants can -never- be as economically efficient in any field as free capitalist economies are.