It would be way too stressful to feel like you have to hit a high rank in three different formats. Plus, if they delivered rewards for all three, you can bet Blizzard would just cut them all by 66%, so it wouldn't matter anyway.
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"Why, you never expected justice from a company, did you? They have neither a soul to lose nor a body to kick." -- Lady Saba Holland
Yeah I think the pressure it would put on wouldn't generally be something the community would welcome. I coukd be wrong but I can imagine far more complaints than people embracing it.
I do think the rewards are poor though. Probably the area of the game if be most critical of. I don't rank up for the rewards at all, I don't even think about them, they are so meh. It's also why unless I have a drive to, for the sake of it, I don't actively bother for legend. What is it? An extra epic or something? It's not a drive, for me at least, in the slightest. I think they could do with upping the rewards in some way, I don't see how they actually support people playing the game.
Maybe they are decent for pure free to play players but i find them so trivial and meagre.