I’ve seen objections to it on religious grounds from the reason stated, but I could absolutely see it being opposed due to financial reasons as well. It insurance is forced to cover it, I’d expect those costs to skyrocket in the short term.While you are correct about the procedure I do not believe that is the reasoning they killed the bill. Based on my limited digging. I believe it was a financial decision. And not all repubs believe it was the right one. Trump and several other support government or insurance funding it.
From where I sit, this is a financial battle being had, not a morality one.
On the flip side, if it becomes more common, I’d expect the cost to drop as more r&d is put into it to develop better and more efficient and effective technology to produce improved results. Currently the success is around 20%. Improving that would be a huge benefit in my opinion.