One can just look around the world to see the benefits of the public model Vs private. Universal health care, quality of living standards for the poor (in both developed countries and upcoming counties like China), Norway's national sovereign fund, there are tons of examples where the public model has uplifted and improved the lives of the many Vs the rich and fortunate few.
Yes it's correct that private companies and individuals will run off and stash money overseas if you tax them; that's why public service are public run in the first place so that we aren't over a barrel and can tax these entities appropriately regardless of what they might do. At the end of the day their own greed will ensure they'll want to invest back into our countries where their investments are safe anyway.
You can just literally take the ownership of a portion of the stocks and investments off them and place them in control of a government run sovereign investment team instead. It's not exactly hard to figure out what these are worth at any moment anyway, realized gains or not, that's what the stock market tracks for us and what they use to estimate worth and use as collateral for loans with banks. If banks trust this way of doing it then so can we.