Summary of why sovereign wealth funds are generally a bad idea: the governments don’t like to do things that could potentially harm their investments. If a government has large stakes in cigarette companies, they’re going to be resistant to regulate them.

There’s also plenty of opportunity for corruption. But even with safeguards, there’s going to be opportunities to steer investment towards favored companies and industries and away from those that oppose the administration or otherwise do things the administration doesn’t like (think of efforts to divest from Israel or fossil fuel companies).

“Just invest in the S&P”. Something like this would give substantial power to the index makers. But it also gives preference to already huge companies. Small, unlisted companies would be indirectly penalized by having to compete against companies with government funding.