Why doesn't the GBTC premium get arbitraged away?

For the sake of putting in an answer:

1. Assuming this is a pure BTC-universe action. So this only applies to someone who has a pile of BTC and is keeping it long-term. So, you are considering BTC "a currency" - you have no concern with, care about, or involvement with, the ever-changing exchange rates between BTC and AUD, EUR, JPY, USD or whatever. You have "an account" with a pile of BTC in it. You're BTC all the way down.

2. Assuming the facts as stated (which is all one can do on this site with any question),

3. The mechanism is this: (i) today buy a GBTC. say it cost 100 units (ii) wait six months (iii) sell it and get 130 units

4. Then ... yes ... as far as I can see, and given point 2, it is an arb.

{Regarding then the question "Why isn't this arbitraged to death?", I simply don't know. The only possible downside (I can see) is total structural collapse of BTC. It could be that the 30%/6 months is (apparently) not enough in most folks minds to cover that risk. [To me that risk seems near-zero, but, that's just me.]} ^†

Hence .. ^†, and noting important Point 2 here, I would simply do this today: I cannot see any reason not to.

To repeat: I am answering and only considering this "in BTC", a pure BTC-universe action. (Note that it's completely common these days to use / loan / spend / earn "in BTC", with no reference to any national currency, so this is not strange or whacky.) I don't know, care about, nor have thought about this action also involving ordinary currencies. IE, I am completely deleting/ignoring point 1 of points 1-5 from the question. I'm answering this "in BTC only". So, this only applies to (one of the many people/institutions) who have and are keeping a pile of BTC, with no reference to national currency exchange rates regarding BTC.

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^† as an aside, come to think, just as when you put USD in a money market placeholder, it wouldn't matter if there was a total systemic collapse - what would be the difference?!

Apart from the fact that a 6-month lock up (which I'm assuming exists because of your post) is a bridge too far and is probably enough to justify the 30% premium on its own in this case, it seems there is only a single Authorized Participant:

This is a snippet from the private placement memorandum for XLM (so the BTC memo may be different):

An Authorized Participant must enter into a “Participant Agreement” with the Sponsor and a Trust to govern its placement of orders to create (and, should such Trust commence a redemption program, redeem) Baskets. The Participant Agreement sets forth the procedures for the creation and redemption of Baskets and for the delivery of digital assets required for creations and redemptions. A copy of the form of Participant Agreement is available for inspection at the Sponsor’s principal office identified herein.

Each Authorized Participant must (i) be a registered broker-dealer, (ii) enter into a Participant Agreement with the Sponsor and (iii) own an Authorized Participant Self-Administered Account. A list of the current Authorized Participants for each Trust can be obtained from the Sponsor. As of the date of this Private Placement Memorandum, Genesis is the only acting Authorized Participant for the Trusts. The Sponsor intends to engage additional Authorized Participants that are unaffiliated with the Trusts in the future.

No Authorized Participant has any obligation or responsibility to the Sponsor or any of the Trusts to effect any sale or resale of Shares.

Separately, redemptions and private placements to the fund are closed.

From the Grayscale site

• Grayscale Bitcoin Trust does not currently operate a redemption program and may halt creations from time to time. There can be no assurance that the value of the shares will approximate the value of the Bitcoin held by the Trust and the shares may trade at a substantial premium over or discount to the value of the Trust's Bitcoin. The Trust may, but will not be required to, seek regulatory approval to operate a redemption program.

And from the Private Placement section of the Grayscale Site:

So there are a few contributing factors that can explain why this spread isn't being arbed away. Leaving aside the 6-month lockup and living in the fantasy world of indifference to dollar fluctuations, the pool of people who could arb this away is extremely small, one. So you can't exploit this opportunity, if you think that's what this is.