you make it sound like some sort of quest, "kill your best friend and get a free Sharingan upgrade!".

and then Kakashi hears about it from Naruto and goes to recieve the bonus?
sounds kinda dumb, doesn't it? if killing your best friend was all that was nesscery to do to get the MS, then Kakashi would've had it from day one. therefore, Kakashi has obtained it after the time jump (remind me, have we seen post timejump Gai?), through one means or another, but not from Obito's death.