It bears note in this regard that the cost of
an IUD is nearly equivalent to a month’s full-time pay for
workers earning the minimum wage
The IUD is one of those things which have a high upfront cost, but they last a long time and so will "pay for themselves" eventually. This alone might pull some weight in the "a compelling governmental interest" area, but she doesn't seem to make this point. Her gist is that it is a form of contraception that some women want but they opt out when faced with the expense.
Life is full of these kinds of trade-off: A washer and dryer are expensive but their convenience and cost savings over a laundromat make them worthwhile. That does not mean the government should buy them for us, or especially; to force our employer to buy them for us.
The whole opinion is here: