Remedy for Hobby Lobby decision?

This is also another example of of the government taking a sledge hammer approach to a problem. Can someone tell me why this is considered a rational policy:

Problem: Some small fraction of women cannot afford birth control.
Solution: Force employers to provide birth control regardless of whether the employee can afford it or not.

A more rational analysis would be:

Problem: Some small fraction of women cannot afford birth control.
Solution: The government provides birth control for women who cannot afford it.

Hell, even this analysis is more rational:

Problem: Some small fraction of women cannot afford birth control.
Solution: The government provides birth control for all women.

I know birth control is a serious topic, but it’s something pretty much every sexual active adult needs, and it’s not terribly expensive. We don’t require dental plans to pay for toothpaste or dental floss, afterall.