If this is run anything like the CPP, it will underperform both the market and their own benchmarks yet lead to executives awarding themselves huge bonuses.
Over the last decade (and even prior to that) CPPIB has been the best performing fund of its kind. National pension funds have different risk tolerances and investment guidelines that someone's personal portfolio or a family office. Thanks to CPPIB, Canada does not have have a giant unfunded pension liability (unlike our neighbors to the south). It has been an enormous success story.
The Australians seem to have the best model overall though. Mandatory payments in to private investments has made them very wealthy.
The UK system takes the national insurance contributions of workers but doesn’t invest them in anything on behalf of the individual. So despite decades of payments you technically have nothing at the end and survive on the goodwill of the government and current taxpayers. That works right now because of the population pyramid.
Canada definitely has a better system than that.