How do we fix surgery?

The fact is that with the modifiers in RAW a low TL surgeon can't even perform basic surgery, and any surgical failure is comically, ridiculously damaging. It'd be simpler to say "you can't do surgery before TL5".

For example, removing an arrowhead at low TL:

-5 low TL tools, -3 no sterilization, -2 no anesthesia, -3 torso or head injury.
Total: -13

This means TL3 surgery to remove an arrow will always fail and deal 3d6 damage to the patient pretty much no matter what.  Leaving the object embedded is initial damage again every 24hrs while it's lodged, so the best way to deal with a barbed arrow is to just yank it out, 50% damage is less than both of those.

What about trepanning? To reduce pressure on the brain to ease recovery of a patient with a concussion. This was a common practice, and was done all over the world. Relieving pressure on the brain by removing parts of the skull is done even now.

-5 for tools, -5 for no physician, -2 for no anesthesia, -3 for no sterilization and -3 for head surgery.
Total: -18.

Even if this low TL surgeon had an entire surgical team in the best facility possible with the best tools possible at the time that'd be like a +6, and it's not routine because surgery never is. That's still -12. Considering 14 or so is supposed to be 'professional'... No. GURPS is an effect based system and this is just wrong. So under the absolute best conditions the surgeon has like a 9.3% chance to perform this correctly without killing the patient, to simply remove a small piece of skull to relieve pressure on the brain. This seems just a bit low, and on a failure, we deal 3d6 damage to the skull, which is damage so it's multiplied by the skull's hit location. Doing 3dx4 injury to the target on a regular failure is just utterly ridiculous and suggesting that this is even realistic is wrong.

We have examples of reality of unskilled surgery in modernity and does not deal this much damage. HP damage is serious injury. So why does a surgical failure, not a critical failure, but a regular failure deal 3d damage? It's utterly insane to suggest that a regular failure at torso surgery can deal more damage than stabbing someone in the heart with a knife.
The idea that ancient surgeons were nothing but bloody butchers is modern chauvinism. If they were, Hippocrates would have called them out and nobody would have used them, but he didn't, even though there was a rivalry between physicians such as himself and surgeons of the time.

LT surgery rules overstate the difficulty of a procedure (especially compared to modern ones) but understate the chance and lethality of infection. Patients dying during a procedure from the procedure are much rarer than dying of complications down the line. But in GURPS it's the opposite, and Low Tech Surgery is insanely, unrealistically difficult.