I think you're missing the general point, so I'm just going to respond to
one point to see if that helps your understanding of why OP_COSHV is better
than just pre-signed.

The reason why MuSig and other distributed signing solutions are not
acceptable for this case is they all require interaction for guarantee of

In contrast, I can use a OP_COSHV Taproot key to request a withdrawal from
an exchange which some time later pays out to a lot of people, rather than
having to withdraw multiple times and then pay. The exchange doesn't have
to know this is what I did. They also don't have to tell me the exact
inputs they'll spend to me or if I'm batched or not (batching largely
incompatible with pre-signing unless anyprevout)

The exchange can take my withdrawal request and aggregate it to other
payees into a tree as well, without requiring permission from the

They can also -- without my permission -- make the payment not directly
into me, but into a payment channel between me and the exchange, allowing
me to undo the withdrawal by routing money back to the exchange over

The exchange can take some inbound payments to their hot wallet and move
them into cold storage with pre-set spending paths. They don't need to use
ephemeral keys (how was that entropy created?) nor do they need to bring on
their cold storage keys to pre-sign the spending paths.

None of this really works well with just pre-signing because you need to
ask for permission first in order to do these operations, but with OP_COSHV
you can, just as the payer without talking to anyone else, or just as the
recipient commit your funds to a complex txn structure.

Lastly, think about this in terms of DoS. You have a set of N users who
request a payment. You build the tree, collect signatures, and then at the
LAST step of building the tree, one user drops out. You restart, excluding
that user. Then a different user drops. Meanwhile you've had to keep your
funds locked up to guarantee those inputs for the txn when it finalizes.

In contrast, once you receive the requests with OP_COSHV, there's nothing
else to do. You just issue the transaction and move on.

Does that make sense as to why a user would prefer this, even if there is
an emulation with pre-signed txns?
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