If they don't want to push down the prices with excess supply, they'd have to sell very slowly. Like France did.
The arb means you’re still suffering a price difference. You’re just paying “the market” to solve it for you.
Related. Not equal.
In reality markets aren't perfect, and also you'd have to take into account the benefit that doing things digitally is much faster, so it won't actually be equal. But in the magic world that economists live in it should be.