In politics as with life, most issues and events aren't simply black and white. Unfortunately for abortion, this has become the case. Liberals in general support no restrictions on abortion and wish for abortion to be legal up until 36 weeks of pregnancy. This is ridiculous position and at this point in the pregnancy, the issue of abortion switches from one of privacy and personal freedom, to one of immorality. Mainstream conservatives on the other hand are equally as radical when it comes to abortion as well. Conservatives have now reached a point where abortion should remain illegal under all circumstances, even instances of rape, incest, and if having a child is a danger to the mothers health. By polarizing this issue, both political ideologies have prevented a happy medium from being achieved when it comes to abortion.
When regarding abortion, it should be legal on request up until 16 weeks of pregnancy. 95% of abortions happen within the first 16 weeks so this wouldn't really effect abortion rights all that much. This law would reduce the immorality of abortion by prohibiting third trimester and a good deal of second trimester abortions when the baby...
Actually that's not true. Most pro-choicers are fine with leaving Roe the way it was intended, which bans elective abortion at 24 weeks -- so it's already illegal at the end of the second trimester, and the entirety of the third trimester. As someone who actually does believe in no restrictions, I am in a very small minority amongst Americans. Most pro-choicers are already what you'd call relatively "moderate."
Further, most anti-choicers still make an exception for rape. This is mind-boggling to me, since if they supposedly think it's a "life," that's like saying that if someone assaults me, I can kill my own child in retaliation. It makes less than zero sense, but then again, they were never really about protecting fetuses. They're about punishing women who enjoy sex, and since rape is not enjoyable, they get a pass. But anyway...
So, right out the gate, you've represented this dishonestly, on both sides.
But I'll tell you why I don't agree, either with you, or with the majority of my own side.
Firstly, we already know what happens when you take away the restrictions. You need look no further than Canada, which is one such place.
You know what happens? Nothing, but for one thing.
Women die less often.
Women almost never abort for any reason other than medical necessity once you get past 18 weeks or so. The red tape holds them up, and sometimes cost them their lives, because they can't get an abortion unless they prove their "need," which sometimes involves waiting for them to be actively dying before anyone helps them.
But late-term abortions don't increase if you take away this red tape. In fact, Canada has just the same rate of late-term abortion that the US does. Because women don't abort 6 months into pregnancy for elective reasons.
Forcing women through red tape to prove their medical "need" does nothing but result in women dying while they're waiting for some stuffed shirt to sign off on the paperwork.
But more philosophically speaking, I will just generally never accept the argument that someone who is being used and harmed against their will ever loses their right to revoke consent and take all action necessary to end the harm, including killing. For the sake of this argument, we'll say I accept that a fetus at 16 weeks is a "person." I find that debatable since it doesn't even have a brain or lungs, but whatever.
When it comes to protecting oneself from harm, in most self-defence law, the intent of the offender is irrelevant -- the right remains even if the attacker is so mentally disabled or insane that they have no idea what they're doing. Even if it's a child. Even if it's a victim of coercion only acting against you because they have a gun to their back. It doesn't matter. You still have a right to protect yourself from an objectively existent threat, even if no ill will is ever intended.
So why is it any different with a fetus?
I've helped women in some really sick situations, like being held hostage or beaten into immobility to prevent them from aborting, and by the time they escaped, they were near the cut-off you propose. It's rare, but it happens.
Do I wish to destroy what's left of these women's minds by telling them, "No, we are not going to allow you to regain control of your body"? Sorry, I can't live with that.
Some things are too important to compromise. The right to protect your body is one of those things. "Centrism" is not always reasonable, like when it requires you to take away someone's right to life and freedom in order to enforce it. Just becomes something is centrist doesn't make inherently more ethical. If anything, sometimes being a "centrist" is rather ethically cowardly. Just because something's not pretty, or black-and-white, doesn't mean it's not still a right.