Yes, in order to get price reductions (after your final payment)...you must book Early Saver.
However, if the price reduction is large enough (and cabins are available) even without Early Saver...you can ask for a free upgrade AFTER the final payment.
Carnival did away with OBC AFTER the final payment when they implemented the option of Early Saver.
Cruising is like airline tickets...the rates can change daily.....
Btw, I believe this has been in place for a year??? So...not a "new" policy....