Not everything in the brain can be taken out wholesale and replaced without causing serious consequences.
Not sure I agree with this. Sure, you'd suffer mental problems whenever we removed something, but I fail to see how this would be any different from, say, treating someone who lost brain function in an accident. I mean I think we can agree that just because someone loses a chunk of their brain in an accident they aren't magically transformed into someone else and the old person in that body was "killed", right? Because to claim otherwise would also be to claim that anyone who has been in a tragic accident and had part of their brain destroyed (or had a stroke and lost part of their brain function, or had a brain tumor and lost part of their brain function) is no longer the same person but is instead some kind of imposter who took over after the old person in that body "died". And considering I know some people who have gone through that (and have mostly recovered from their injuries), I find that result both mentally abhorrent and kinda offensive, to be honest.
I mean at this point with the amount of humans on the planet we've had individuals who have suffered pretty much any type of localized brain injury imaginable and bounce back, up to the point of some people who have literally lost the parts of their brain that have kept them breathing subconsciously and have had to spend the remainder of their (usually short) life on life support. To claim that "oh no, really those people died in their accidents and someone different took there place" seems kind of a strange claim, considering that in pretty much every survival case people have been able to access at least some of their old memories/etc., and that they themselves still view them as the same person. Even massive injuries resulting in persistent vegetative states do have the occasional person wakeup and return to some level normalcy as their "old" selves, albeit often with lingering mental disability baggage.
Medicine has reached the point where it is no longer possible for you to say "oh, but nobody has ever managed to survive as themselves after taking
that brain injury". Even
Phineas Gage, who suffered so much personality change right after his injury that his friends no longer thought he was Gage, after a few years managed to return to the point where he was accepted as just a different take on his old self instead of some sort of stranger in Gage's body. To put it in terms of the earlier remove an arm metaphor, modern medicine has shown that are brains are indeed all "arms" without any "heads". There is no particular bunch of neurons that, when destroyed, suddenly "kills" the old you, just ones that warp or wind you instead.
As for the earlier ship of Theseus example, I'd say that the CAD drawing goes a bit far. I'd probably describe it like this instead:
1) You start with a ship made of wood.
2) Each time you remove a plank you replace it with an identical one made of metal.
3) You now have a (still functional) ship that looks identical, but everything is now metal instead of wood.
4) Now that the entire ship is made out of metal, it has the required internal strength required for you to strap boosters to the sides of it and use it as a rocket ship that flies through space instead of a normal ship on the ocean, something that would never have been possible in the original design.
The idea isn't necessarily that we'd scan your brain and upload you to a computer. We could replace pieces of your brain at a time while leaving the replacements inside your head (ala Ghost in the Shell), and it's only when you reach the point that you are fed up with your biological body breaking down that we actually remove it from your skull and connect it to a robot instead.
And that solves a lot of the moral problems, since at that point your brain is just another part of you in the same way that a piercing might be considered part of you, not necessarily something that is running on somebody else's hardware.