It's probably the trickiest of political issues, particularly because it's so personal to so many. And the problem is that for most people, they look at it from a strictly binary perspective. If ever the ability to compromise was needed, it's on this issue.
I recall reading years ago, a commentary on the subject by Carl Sagan. I ought to dig that up and read it again, because I recall my take on what he wrote was that he was as usual, very reasonable and logical. I believe he suggested the threshold between human and "bunch of cells" be determined by when the brain turns on. (he probably used a more scientific term than "turns on") Something tells me that as is often the case with true compromise, neither side would find that acceptable.
The other key point you make is about the legal aspect of the Roe v. Wade ruling. I agree with you there, it was just bad law. Poorly written, poorly supported. Here's where I'll veer into the partisan ditch! In typical liberal fashion, they were apparently so thrilled at being able to do what they wanted, that they didn't take the time to do it particularly well. That's the primary reason it lasted *only* 50 years. The impeachments of Trump reminded of this same haphazard approach. Strictly speaking, demotards need better leaders.