I wish to respond to some of the more specific points in John Oliver's video, but before I tackle that I wish to make a general point about abortion access in general. There is a general implication that unless there is easy and close access to abortion, then the right to have an abortion itself is threatened. Obviously I deny that this right should exist, but this argument itself is fallacious and it is easy to demonstrate why.
Allow me an example. I have a desire to see the documentary that Oliver references in his video. Unfortunately, the closest screening to me is about 300 miles away. It would be prohibitively costly both in terms of time and finances for me to view this documentary that I really want to, and in fact have a right to see.
Furthermore, what if I contacted my local theatre and asked them to host a screening? They then check into the possibility both report back to me that it would be prohibitively expensive for them to host. They would love to, but the money that they would have to invest in order to show that documentary is not worth it.
Would any of these facts change the "right" that I have to see a movie of my choosing? Am I being denied my constitutional rights because someone in Chicago has access to this movie and I do not? How close does the viewing need to be to me before my rights are considered protected?
Likewise, even if abortion is not locally available or convenient does not indicate that one's constitutional rights are being fringed upon. Roe v Wade did not guarantee abortion to be a locally available procedure.
This is not to argue that all of the so-called TRAP laws are wise in this fight, but the mere fact that abortion may be more difficult to obtain does not an infringement of any supposed rights.