This change would have three major effects:
1) The average time / effort to gain a rare would decrease and so would their rarity. This would be easily adjustable by using a higher number of tokens (as Jellyfish already suggested).
2) The variety of rares would decrease. Everyone seems to hunt Pulverizers and Eternities and occasionally Eagle's Eye, Discord or Trident - but there won't be a lot of i.e. those vampiric daggers (shame on me - i don't even know the name ;-)) out there if everyone could choose the rares he wants.
3) The Randomness would be removed. One wouldn't depend on luck, simply knowing when the next rare's gonna pop up. While this might be less frustration sometimes, it would imho vastly reduce the happy fealing you get, when that Miracle (or whatever) is finally yours.
The last point being the most important to me, I personally must admit that I don't really like that idea.