Coinbase published a blog post today about how they view a transition to post quantum cryptography for Bitcoin. This is relevant because:

Coinbase is one of the largest crypto custodians in the world and holds ~5% of all BTC in existence.

And I think they are rather understating how much Bitcoin they hold.

Anyhow, here are the interesting points:

1. Preparing before certainty. We believe it is important to begin preparing well ahead of any CRQC announcement. Bitcoin consensus changes and ecosystem migrations can take years, So it is important that we begin this work now.
2. Separating the "container" from the signature. In our view, a PQ output type design that allows one or more PQ signature systems to be introduced, replaced, or supplemented without a complete redesign would serve the ecosystem well. P2MR (BIP-360) and P2TRv2 appear to offer this kind of flexibility.
3. Staged protection. We would welcome an approach in which active wallets can use a PQ-capable or hybrid construction before the final legacy-signature policy is settled. One possible transition design is a 1-of-2 construction: the same funds have two alternative spending paths, one authorized by a classical ECDSA/Schnorr key and one authorized by a PQ key.
4. Use of state. While stateful PQ signature schemes could be smaller and faster than stateless ones, managing state in digital signatures is notoriously error-prone and could even lead to forgery. If stateful signatures are supported, we think it is important to also have a stateless option available.
5. Robust implementations. We hope the evaluation process will place strong weight on deterministic, cross-platform verification, constant-time implementations, clear parameterization, and resistance to signing RNG failures.
6. MPC-friendliness. For Coinbase and many of our customers, MPC-friendliness is an important consideration in the choice of PQ schemes. When implemented effectively, MPC can provide strong protection against key theft, and it is an important layer of defense for large organizations that face constant attacks on their infrastructure.
7. A path for wallets that migrate late. If Bitcoin eventually limits or ends ECDSA/Schnorr spending, some wallets may not have moved their funds to PQ-safe outputs by then. We believe it would be useful to consider whether and how those users could migrate their funds afterward, while recognizing that the approach and its tradeoffs remain open questions. In our view, that discussion can proceed alongside, and independently of, the technical work to add PQ signature support, so it need not delay progress on that work.

They are fairly supportive of BIP 360 as well as hash-based signatures like SHRINCS.

They also have a little section on the burn vs steal debate, but I didn't feel that it had very interesting stuff in it.