All my decks are Legacy legal, and when I heard of this rule, I couldn't help but think of a multitude of ways that this can be used to improve my decks. For starters, I can use
Mirror Gallery without the monumental risk of blowing up all my most important cards from someone using a single artifact destruction. I have a deck that uses it already, and a number of my cards are specifically there to protect Mirror Gallery because of the unjustified risk that was associated with it. Many of my decks benefit automatically from the rule improvement, since they are dependent on one or more legendaries and no longer have to suffer the severe overkill drawbacks associated with the theft and cloning of legendaries. It certainly expands on player freedom and allows for more strategically viable options when playing and deck building.
This one guy went on an elaborate rant about the possibility of
Emrakul being played from
Show and Tell to take four turns in a row and then STILL having Emrakul when it was all over.
The main issue with this is that it's a needlessly complicated scenario. If you get Emrakul out, you're going to win most of the time. The problem is that Emrakul, like most of the other Eldrazi cards, is brokenly powerful. Quite a few people in Legacy will simply quit if you play Emrakul, and that's the fault of the card, not the legendary rule. While there are certainly more avenues open to a player with this rule improvement, getting multiple Emrakuls out in succession isn't a meaningful possibility when you generally win with the first one.
Also, a lot of people who play Emrakul decks do so using "take additional turn" cards, like
Time Stretch, just to augment their turn advantage. The addition of the legendary rule isn't really going to make Emrakul decks any more powerful than they already are; it doesn't help them get Emrakul out, which is the most critical part of their strategy.
I'd say it's fairly undeniable this impacts Legacy quite a bit, and only taking game balance into account, it's a positive change. How it affects the lore is of little concern to me; it could be argued that you shouldn't even be able to play a second legendary card if the first is out already (which is how it used to be originally). Taking it further, it could be said only one copy of a legendary card should be allowed in your deck, because there can't be multiples of them. When there's a serious conflict between lore and gameplay, the lore needs to adapt to the gameplay, not vice versa.
The reason I questioned the impact on EDH is because of the difference in the ruleset; there can only be one of each card in your deck, which automatically prevents the possibility of having duplicate legendaries in hand. This on its own resolves most of the impact that the rule change could possibly have. Additionally, according to the rules page which was linked, the house rules commonly used either restrict people from using the same general, or don't subject generals to the legendary rule in the first place.