Yes, that's why so many companies leverage third party 401k companies to invest the money in.
The Postal Office and some other large parties (eg. GE and GM and the US Government) have historically refused to use a third party because they don't want to transfer the funds (as they still leverage these funds), thus for every employee you hire, when they're 18 or 20, if you promise them retirement (which USPS does, even for their most junior employee) you have to start funding their retirement.
Retirement funds are basically a savings account for your employees, you can't say, I'll hire you today and I'll start fund your retirement from operational funds when you need it. There is compound interest. So if you promise $20 today and you DON'T FUND (which is what you're proposing), 40 years from now you have to start paying out $2000.
Where do you think that money comes from? Taxpayer of course which will have to bail out these funds as they have been doing for the last 20-30 years, the USPS needs to make up a LOT of money as they still aren't fully funding their existing pension funds from retirement funds, they are STILL asking Congress for money to fund the current retirees. So yes, for every employee they hire today, they have to fund twice the amount of retirement to cover current and future retirees because compounded interest over the last 50 years.