If IRROPS are likely, or in play, you'll be able to go earlier, or indeed later, if it helps the airline.

Otherwise, the equivalent of your "SDC fee" is the change fee.

Given that in NA, they fill up the "First" cabin with free upgrades, there's more of a culture of giving away something of nominal "value" for nothing on the day of departure (or shortly beforehand). You could argue this incentivises your customers to pay less (buy Economy, fly "First"; buy a cheap ticket at an undesirable time, fly out on a more expensive ticket at the actually-wanted time - here I'm assuming the SDC fee is less than it would have been to buy the seat you wanted outright from the start?). That's never taken off over on this side of the Atlantic.