Private companies don't really fully fund their pensions, but during the period where pensions were common in private companies, those companies were expanding in revenue and headcount, so it was ok. Was.
High-risk private enterprises don't do pensions now (can you imagine a Zynga Pension Plan?). Approximately everyone has shifted to defined-contribution from defined-benefit. The problem is USPS and the fully-private companies with legacy pension plans are both in long-term decline and have underfunded pensions, but USPS is particularly large in workforce and obvious in long-term decline (and political).