Fox vs Marth, game 1 YS. Fox wins and bans FD. Marth goes back to YS. Marth barely wins on a 2 stock comeback. Marth realizes something new about the match-up that changes his perspective of the matchup on that stage. He bans FoD and would rather play on a larger stage based on this new knowledge of the opponent's style. He doesn't mind DL because 1) he likes the match-up on that stage or 2) he has a secondary he would play there. Another valid reason for not agreeing back is simply for a change in pace, for example, you think you can adapt to new stage strategies faster than him.
Under the current rules, fox could ask marth to go back to YS. If marth would rather play there than another "worse" stage (BF or DL) then he can agree. If he doesn't want to, he isn't forced to.
This rule change would assume that because a player chose the stage he lost on as a counter pick that he would agree to that stage no matter what, which is not the case. Forcing him to agree (which is what this rule does) does nothing but dissuade players from returning to a stage, because if they win it would give the opponent additional resources they wouldn't otherwise have (stages available to counterpick is a resource). In the current rules one can return to that stage knowing that if they win the opponent's options are still partially limited.
DSR makes it so that you trade one resource for another -- an available stage choice for a point towards the final win. With this rule, returning to a stage gives resources back to your opponent when otherwise they wouldn't have.
Really, this rule isn't a big deal, it doesn't change much, but no matter what it only favors the winner of the first game and restricts options of the loser of the first game. In my opinion, the ability to choose the next stage is an advantage enough, and the ability to request the stage again is enough for the advantaged player.