Got to thinking about this rule a bit and was trying to figure out cards and things that can take advantage of this other than the obvious ones like powder and bazaar and had 2 thoughts.
1 - This mulligan does have some corner cases where it is not strictly better, and many that are. The one thing I can think of is that on the mull to 6 you technically see the same number of cards, but you have the option not to bottom one on a keep. Additionally if you put the scry on top you are protecting it from duress for a turn, where as in the new rule it has to be in your hand.
2 - Squadron Hawk seems very strong to me now. I know that sounds silly but because you get to choose to bottom the cards you don't want, you basically always get to put other copies of hawk back and ensure the copy you keep is a 2 mana 1/1 flying draw 3 (and not 2 copies of a 1/1 draw 1). Obviously the power of this card is more about Jace or brainstorming the other copies away but I could see it getting a real boost if this mulligan rule took effect.