But if you want to do a sidechain BTC transaction faster, you swap it for a small premium with someone who already has BTC on the sidechain and is planning to long term hold, or swap with someone trying to go the other direction. What you pay them will be small due to the mechanics of arbitrage. They'll just look for some small fee because to them if they're already long term BTC holders its basically free money, like interest on BTC to move funds back and forth and provide liquidity service for sidechains. The $ exchange rate is immaterial, the best candidate for sidechain liquidity provider is someone who is anyway holding their own or other peoples BTC for long term storage.
The longer the time-preference, the bigger the possible spread because of the increased risk of volatility over time. Your SC can offer varied time-preference risk for fee rates desired by different trading strategies. Like Certificates of Deposit offering different interest rates depending on deposit length.
There isnt BTC denominated volatility because you're comparing BTC to BTC, unless the arbitrageur is not anyway a long term BTC holder, and so looking at BTCUSD volatility, in which case you would be right; however BTCUSD volatility is sufficiently high that holders of BTC could undercut non-holders taking BTCUSD exposure solely to gain the arbitrage profit. As I said
the best candidate for sidechain liquidity provider is someone who is anyway holding their own or other peoples BTC for long term storage.Note also re your CoD rate comparison, you can buy forex forward contracts for below the interest cost of borrowing the money to exchange now. This is because the market maker can discount by using interest to move in the other direction.
The same thing would take place in a mature arbitrage environment between sidechain and bitcoin, the arbitrageur can do it below the amortised 2wp fee cost, because he can hold positions in both chains and cancel out the flows in opposite directions, just as the forex forward contracts. If you're willing to wait for p2p trade you may even do it at bitcoin tx fee cost only using cross-chain atomic swaps (faster than 2wp but slower than via arbitrage agent).
Or do the 2wp yourself direct if you're willing to wait.
The interesting thing is the arbitrage can be both faster and cheaper than the 2wp, and trustless via smart-contracts. And because its a p2p blockchain on a technical* level anyone can do arbitrage without permission from anyone.
(*Technical because there is also regulation: regulations may apply to arbitrage service; though I do think an interesting future potential is that regulators in more forward-looking jurisdictions will exempt zero-trust operations from regulation.)
Adam