The greatest tool for building wealth is time. That is an asset that organizations have that individuals do not. Look at the endowments of top tier universities. There is no reason that governments can't do the same and benefit from the long lifespan of a non-human entity.
This has the benefit of aligning government interests with the interests of the people. It also makes government more supportive than punitive as revenue only increases by cultivating an environment for business to flourish.
I think the sovereign wealth funds have a lot of the same problems the social security has. Politicians will borrow against it and never pay it back. From what I have heard some middle eastern countries had a sovereign wealth fund that was mismanaged, I guess if you have a competent government it is fine, but you don't always get to decide that.
Overall, I agree with you that both of these are a good way to distribute society's prosperity to the people.
One potential way to mitigate these risks is to have the fund be set up with a strict breakdown, say, 20% of the dividends can go into a pot that the government can use for discretionary spending, and 80% goes to the people equally divided as a dividend, and the only way to change this percentage is with a 2/3s majority. The percentage split and the consensus threshold are certainly debatable.
We've done that, except the dividends to go to a few rich families instead of to everyone.
Alaska's Permanent Fund is only allowed to invest in Alaskan companies and is "only" $75B in size (https://www.alaskajournal.com/2021-02-24/fund-continues-bull...), and even then an Alaskan resident would have received $2,000 in 2015 simply for existing: https://pfd.alaska.gov/Division-Info/Summary-of-Applications...
By scaling up the size and scope of the fund, you can conceivably get to a place where the dividend can work out to $10k+ per person per year.