The reason that they needed to be pre-funded is because the USPS was shrinking and is expected to continue to do so.
What happens with a private company that’s shrinking or going under is that people who have a pension plan risk winding up without their pension.
With the USPS, it’s a quasi-governmental agency. Strictly-speaking, the government isn’t on the hook for the pensions…but it’s a pretty good bet that if the USPS can’t cover pensions, then USPS workers are going to be asking the government to cover it down the road. This ensures that it’s the USPS that pays for it, rather than it running up a huge debt, filing for bankruptcy, and then dumping it on the taxpayer.