You may be right that the insurance companies have been quiet on this mandate because they might think that it will be a cost saver for them in the end.
My personal feeling on this is that the only outcome of this mandate is higher insurance premiums to cover the costs.
The people who currenly use contraceptive will continue to use them and the people who don’t use them will continue to not use them.
There won’t be any less unwanted pregnancies or births, or lower overall healthcare costs as a result of this mandate.
There are ways to lower the costs of healthcare, but this mandate is not one of them.