I don't think a majority of sBTC to BTC volume will be peer to peer but rather will involve a swap provider.

Consider.

1. Anyone can deposit into the side using an M5 Deposit transfer of BTC from-main-to-side.

2. M6 Withdrawals take time and require bundles be proposed and accepted.

This results in a situation where sBTC to BTC pressure can build but BTC to sBTC pressure cannot build. From this I assume sBTC -> BTC fees will be higher than BTC -> sBTC. The fees will attract service providers to arbitrage. They will need BTC to swap for sBTC. To transfer back out to have enough BTC to continue the arbitrage they need to wait for a withdrawal. They are effectively locking up BTC as sBTC to earn the withdrawal fee.

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Arbitrage traders are not platforms or service providers. There will be a slew of arbitrage traders ready to charge a premium to swap out of sBTC, but they are not 'service providers'. They are not trusted, centralized, or able to interfere with your exit from sBTC. Anyone with a little money can become an arbitrage trader, so there will be many traders competing for volume, so they wont be able to charge too much of a premium or risk losing business to the other arbitrage traders.

Yes, sBTC -> BTC pressure may build, and arbitragers may charge a premium to exit, but if that premium gets too large, it will invite more liquidity into the market, and cause the premium to drop back down.

This is much more desirable than the trusted mint/provider situation we find ourselves in with Lightning, Cashu, Fedimint, etc