Aside from how the purchases would be financed, once you had the fund owning these assets, there would be pressure to distribute them to individuals. Then the program is kaput.
The required tax increases are not large and not needed now. Even with present, pessimistic projections of growth, after-tax wages in 2030 should still be much higher than presently, so "our children" will be richer, even with the higher tax. Under the current structure of the program, they will also get higher benefits.
The shortfall is attributable to longer life expectancies. If you expect to live longer after a fixed retirement age, it's reasonable to pay more taxes against that contingency.