For what it's worth, my impression is that the reason it's not regularly administered is because doctors think it slightly increases the risk of complications for the mother (e.g. bleeding) and would make the procedure slightly more expensive and time-consuming. That, plus the assumption that the drugs given to the mother during the procedure are sufficient. Also, there have been efforts by pro-life lawmakers to draw attention to fetal pain, though this is probably a tactic to increase anti-abortion sentiment in general.

From this 2015 Washington Post article:

"Fetuses are routinely sedated during surgery, for reasons beyond the fear that the operation might cause them pain. Anesthetics stop a fetus from kicking around, making the operation safer. And though a fetus might not be conscious of pain, its body can respond to pain and stress in ways that interfere with its recovery. Painkillers alleviate that problem. That can happen directly or indirectly. During fetal surgery, women typically receive general anesthesia or sedation, making them unconscious or semi-conscious and pain-free. These drugs pass through the placenta to affect the fetus. For more involved operations, doctors inject extra painkillers directly into the fetus...

For as long as the fetus is alive during the abortion, it will experience some anesthetic effects depending on what drugs the mother receives. But would indirect anesthesia suffice to provide the “adequate relief” from pain that HB 479 demands? Just to make sure, Olszewski would prefer that fetuses are anesthetized directly during an abortion. He says that doctors can readily learn how to use an ultrasound-guided needle to deliver a cheap dose of painkillers to the fetus."

My weak intuition is that pro-life people would support anesthesia. For one reason, they may support it precisely because of the reason you give that pro-choice people do not support it (that is, the implications of moral personhood some people may infer). On the other hand, one counterexample to my intuition is the analogy to how some animal rights activists oppose welfare reforms or at least discuss them with a negative tone, due to a more absolutist or anti-incrementalist position. 

But perhaps more importantly, if it's true that pro-life people generally would support it, I would expect that to make it less tractable, because there's a risk pro-choice people would react and be polarised against it if it was seen as a pro-life political weapon. 

In the US, abortion is often a private-pay surgery, and so keeping costs low is seen as more of a concern than with procedures for which insurance is usually footing the bulk of the bill.

I'm not sure how difficult fetal anesthesia is -- a skim suggests IM fetanyl might be used here. Injecting into the wrong area by accident seems easier than for a newborn, especially where the anesthesia is not performed by an experienced fetal surgeon.

I think the comparison group should be based on principle, rather than pragmatic considerations of which bucket you'd rather divert funds from!

If it's true that GHD funds should be diverted to AW funds, then they should be diverted to AW funds, not to a very poor substitute for an AW cause.

I personally think it isn't obvious that GHD funds should be so diverted, precisely because of their greater potential for flow-through effects. But of course if that is the basis for GHD funding having a lower "bar" than AW funding, it cannot justify applying the low (GHD) bar to this cause (which lacks potential flow-through benefits).

It's been a while since I looked through it, but my impression is that the billion neurons of the fetus are hanging out on the cortical plate and havent fully migrated to their final configurations, which may affect things. My impression was that the cow exhibits far more evidence of sentience than the fetus, for example giving much more similar brain activity to a grown human on an EEG. However this was from a skim a few months ago, so I would be interested in a more thorough investigation. 

I agree that this probably wouldn't be competitive with animal welfare. However, if we're holding it to the standard for suffering-reducing interventions for humans, it could plausibly be more competitive.

 I think that even for someone who only cared about the suffering of humans and human fetuses but not animals (a hard position to justify philosophically), it would still be a hard sell, for the same reason as before: The suffering of humans can occur over long periods of time, whereas an abortion is relatively quick. In addition, even if a 13-week fetus experiences some pain, would it compare in intensity to a grown infant? 

I think the only way it could compete would be if the intervention was very cheap and easy, like if there was an easy way to persuade a medical group to change their recommendations. 

Nonetheless, I think it's a topic worth at least thinking about! It's important to be sensitive though, as this is a justifiably emotionally charged topic for a lot of people. 
 

Again, I think this post is missing nuance; for example:

1. Induction of fetal demise is done through a variety of means in multiple respects--different medications are given (i.e., digoxin, lidocaine, or KCl) via different routes (i.e., intra-fetal vs. intra-amniotic). (Given that lidocaine is a painkiller, I could see a different version of this post compellingly making the case that to the extent clinicians have discretion in choosing what agents to use to induce fetal demise, they should prioritize using ones that are likely to have off-target analgesic effects.)
2. So, the link you post refers to a small minority of abortions, as it's only routine to inject the amniotic fluid (specifically) with potassium chloride (specifically) prior to the delivery of anesthesia in some second-trimester abortions.
3. Potassium chloride is a medication that's routinely given via IV to replete potassium. The dose has a significant effect on how painful this is, as does the route of administration; people tolerate oral potassium fine. Importantly, the fetus is not even being given KCl intravenously (vs. intra-amniotically or intra-fetally), so it's hard for me to infer from "it is sometimes painful to get KCl via IV" that it would be painful for a fetus to get potassium via a different route. Correspondingly, then, I don't think the "inflames the potassium ions in the sensory nerve fibers, literally burning up the veins as it travels to the heart" applies.

Sounds very difficult when deadly drugs like fentanyl, midazolam and propofol can easily be injected through an intravenous line. You can't get an IV line on a baby in-utero, I think that's why injection into the heart is done in that case.