The biggest reason why women should not be denied this part of healthcare is because it is not always used as it might have originally been intended. Many women use it to control their periods and some even use it to save their lives by preventing some female reproductive cancers.
Birth control is so relatively inexpensive that I don't see why an insurance company would not want to cover it for one of its policy holders unless it is for the religious beliefs of the providers which really do not belong in a contract situation. It seems clear that a woman who can control pregnancy can control other aspects of her health on many levels that can save the insurance company money. My guess is that unless they want to make pregnancy also an option and not cover anything that results from that, they should pay for birth control.
Since birth control is not typically medically necessary, no, I don't think it should be required that all insurance companies provide it. However, it seems to me it would make fiscal sense for them to cover it. Birth control is much cheaper than pre-natal care, birth and delivery and then 18+ years of providing that child with health care.
Having a child should not be an accident. It can be avoided if proper care is used when deciding to have sex. Insurance is normally for unusual circumstances which were not planned. If people were smarter and used protection or before having sex made sure that they could take care/wanted a child then there would not be this problem.