Anonymity - this is likely to (and WILL) be a very attractive feature of some alt-coin (the only reason bitcoin would even dream of implementing it would be if not implementing it would cost them SIGNIFICANT market share and threaten its future dominace, which is unlikely due to the network effect and the fact that most bitcoin users nowadays don't feel the need for ABSOLUTE anonymity). Many services which rely on or prefer anonymity would accept this currency directly, and users only using crypto for those services would hold the currency directly rather than buying bitcoins. Liquid exchanges would be very likely - decentralised, anonymous exchanges would make users of the anonymous currency even more confident.
Thanks for the confirmation of the logic I presented upthread on the value of anonymity. Won't be for everyone, but some want it.