That's because when the government forces the cost on private businesses, that hides the source of the increased costs. When the government actually has to raise taxes to pay for it, people can figure out that it's too expensive. If the company raises its prices because of government mandates, people just say "greedy companies" rather than blaming the government. Making the government pay for these things directly is an important part of having checks and balances on the government because people notice taxes.
In other words, "if you make the government pay for it, people will complain about raising taxes" is a feature, not a bug. That's the point--the government should make it obvious that it is taking the money, so the public can decide whether it's really worth it. And sometimes they won't.