Personally, I would like to see everyone get the same legendary, but I am not sure it would work from a balance point of view.
Take your average heroic guild, most of their raiders are just waiting for 5.4 to progress, and as soon as it is out, they will rush to get their legendaries (in days or weeks or however long it takes). Once their full raid has legendaries, raid progress will either be trivially easy, or will have to be balanced around the expectation of full legendaries.
On the flip side you have casual guilds where people are clearing 12/12ToT now, but not working hard on legendary quests (I am in this type of guild now, and it kind of infuriates me that we're held back by people with no LMG). People in these guilds will have a lot of trouble progressing since they don't have full legendaries.
Maybe heroic mode will be much harder than normal modes, with the expectation that everyone has a legendary when you start heroics? That puts a fairly strong cap on progression for newer characters.
Blizz has shown that they don't really care about trivializing non-raid content, so maybe they don't care that giving LFR heroes extremely powerful legendaries will make most/all of their content trivial.