The Texas law which claimed "six weeks" actually meant six weeks from the woman's last period... not the one she misses, but the last one she had.
Assuming that the missed period is usually the first sign a woman gets that she might be pregnant, approximately four weeks have already passed before she even knows... putting the woman in a position to make an informed choice before it gets to be a fetus doesn't seem to be a priority.
I can't speak for the rest of the country, but in NYC, where access to abortion isn't restricted, same-day appointments are common. The procedure itself can be done in about 5-10 minutes.
Any delays are political, not medical.