Now we introduce the concept of time-preference.  For security reasons (rather similar to coinbase maturity which sees you unable to spend freshly mined coins for 100 blocks) the algorithmic peg has a time-delay.

Now if you planned to hold anyway for that period or longer, then you dont care and the situation is unchanged.

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.

Anyone who tried to sell  BTC on one chain for a lower than time-preference cost on another chain would just lose money.