I agree with most of what you say except the 7 weeks thing. While the brain has started to develop, brain activity isn't present until the 13th/14th week, basically the end of the first trimester, start of the 2nd. At this point, there's a heart beat, many organs are functional, lungs are starting to develop, limbs are formed, the baby even starts to suck its own thumbs.
Yeah, that seems more like a sensible line in the sand, the sort of thing that Roe v Wade prevented. Lots of European countries go for limits of around that length of time for regular abortions.