In fact, OG, if the State Pension fund was provided on a "contributions = benefits" basis it would be more than self funding. But that of course would mean that some people would get nothing. The problem is it purports to be a pension scheme (which should pay according to contributions made) but at the same time acts as the "safety net" that you describe for those who have not made their own provisions. It cannot be both.
If it is to be run as a pension scheme then members are entitled to be paid out in direct proportion to their contributions. At present that does not happen. Governments should be honest and say that it is not a pension scheme at all but simply an extension to the rest of the welfare system where those who pay the most in get, proportionately, the least out.