Why not, though?
They're obviously at least partially physical constructs objects given that Shiro could get an arm graft from future Shiro and the magical circuit lineups were a plot point.
Then you have the worms, crests which can be transplanted despite being bunches of magic circuits, Rin transferring her magic crest to Shirou that one time, pedobait Jack's Surgical Procedure is implied to be at least partially mundane, and spiritual surgery can manipulate them too. I'm sure there's several other examples I'm missing, as well.
On top of that, it says explicitly that Rasputin's internal furnace allows him to integrate materials he swallows into his body. That seems like a sufficient loophole to be able to jack magic circuits. You did say Fate was all about loopholes, didn't you?

I'll accept getting nothing from bird because I misunderstood how familiars work apparently but I would argue that the theory is still sound.

That's the meshing of a spiritual body and physical body, which only worked because they're the same person. Circuits are physical and in the soul simultaneously, the issue isn't that you can't swallow circuits and integrate them in your body. The issue is that after you do that the circuits are going to reject your body and freak out which will cause you to kill yourself in what's basically the soul's autoimmune response.

So maybe I shouldn't say you can't integrate circuits so much as you shouldn't.

He's a freakishly robust homunculus.
No soul and all that.

Then he doesn't have Circuits, so he did not summon Vlad.

I'm sorry but he's not in the war.

He's not moving.

He's a clump of mud on the ground.

My condolences.

Well, that was the easiest way to kill a Master. He literally thought himself out of existence like this was Pandora Hearts.

That's bull, but sure, accepting your premise of "the soul's autoimmune response" on a purely artificial human, that still leaves Rin transferring her crest to Shirou as well as Surgical Procedure which both show it's definitely possible to ignore that entirely.
That, and IIRC it was stated one can transfer magic circuits if both subjects in question are synchronized and willing, and a corpse can't exactly resist on either of those fronts.

Well, that was the easiest way to kill a Master. He literally thought himself out of existence like this was Pandora Hearts.

Divided by Zero

Considering Shirou survived turning his own spine into a magic circuit on a weekly basis for years before being corrected by Rin, he tends to throw all odds and probability out the window.

Doesn't matter, still happened.

That's bull, but sure, accepting your premise of "the soul's autoimmune response" on a purely artificial human, that still leaves Rin transferring her crest to Shirou as well as Surgical Procedure which both show it's definitely possible to ignore that entirely.
That, and IIRC it was stated one can transfer magic circuits if both subjects in question are synchronized and willing, and a corpse can't exactly resist on either of those fronts.

Rin made a contract similar to a familiar with Shirou so that it could happen without killing him. Even inside a same family transferring a magic crest can kill or cripple someone if it's not made right and that's because the circuits share your blood, foreign circuits are pure poison.

BTW, the procedure Rin made with Shirou is possible to any decent magus, t's just that if you don't have a Servant worth of Od to spare, you'll screw yourself while giving someone else the power they need. Even Rin got almost screwed when Shirou activated UBW, for God's sake.

EDIT:

Archer's arm also killed him, because the circuit came from a Servant's body. After Kotomine performed the surgery Shirou could already be considered a walking corpse, it was just a matter of time before her became a corpse corpse.

Except, again, a corpse can't resist on either of those fronts.

That's bull, but sure, accepting your premise of "the soul's autoimmune response" on a purely artificial human, that still leaves Rin transferring her crest to Shirou as well as Surgical Procedure which both show it's definitely possible to ignore that entirely.
That, and IIRC it was stated one can transfer magic circuits if both subjects in question are synchronized and willing, and a corpse can't exactly resist on either of those fronts.

A soul's a soul. Homunculi still have one.

Rin explicitly processes it so it'll work, since Shirou goes as far to talk about rejection in his mental narrative not much earlier. There are ways to process small amounts of a Crest so that can be received, but even that's just because Crests aren't entirely normal Circuits anymore. There aren't means of doing that for either the entire Crest or someone else's Circuits proper.

You see that with Touko and her butterfly wings, in spite of Touko being so good at familiar creation that she tricked a planet.

You see that at the end of Apo, in spite of Chiron being a medical genius who transplanted a Servant's heart into a mud doll.

Besides that, if your logic was right then anyone with Spiritual Surgery would be able to just take all the circuits of any dead magus they find without issue. It's not. Transfer of a minute portion of a Crest, which has already been isolated from the whole and isn't Circuits proper anymore, is fine. Transfer of the full Crest or of someone's soul organs, however, is not.

Except, again, a corpse can't resist on either of those fronts.

"Why can't I just take this guy's liver and put it in my body? He's dead so he can't resist."

Fairly sure homunculi have weaker individual souls than humans, though, given that's the justification for the crappy od they get. the "autoimmune response" should be weaker as a result.
And as for the other thing does that mean if Rasputin was to process it using alchemy first he would be able to transplant efficiently?

EDIT: Also you're leaving out the part where there's a readily available procedure to make the guy's liver work for you.

The force of life is weaker, but even if it worked the way you think it does it wouldn't matter. If you have a weak body so you can't stab yourself as hard as a strong guy, your weak body will still die from the weak stab.

Unless you're some sort of god-surpassing genius, no. Something like that would flip magus society on its head. Even Touko, the girl who does that on a weekly basis, can't do that.

EDIT: Also you're leaving out the part where there's a readily available procedure to make the guy's liver work for you.

There isn't that sort of procedure for Circuits.

People with weak immune systems get better odds on organ transplants though.

Congratulations. Your odds will be 2 in 10000 instead of 1 in 10000.

If you really want, then I will roll a 1d10000 when you try to integrate someone's Circuits.

I'm pretty sure this site doesn't have a diceroller yet actually.

EDIT: Actually come to think of it couldn't the large intake of genetic material from actually physically eating a person be integrated as well and used to fool the circuits themselves? This issue is the genetics mismatch, right?

Google

It doesn't, I just mean I'll use an online roller.

I'd unironically be fine with that.

Cool then I'll go with that justification if it ever comes up.