Personally I think there really isn't any incentive for a hardcore toon, they can't trade, stash or use auction and their achievements and titles are character bound. If one dies in PvE or PvP they have to start over from scratch.

While I think a hardcore mode is interesting I feel like it would be better done with different or rather reoptimised maps, similar to how Elite mode scales the difficulty of the mobs etc, hardcore would make the mobs/bosses easier or different (e.g. different attack patterns).
Also I think reworking item drops for hardcore toons would be good, perhaps an exclusive currency or point system earned only by hardcore toons similar to Somberhault, HC toons can use these points in exchange for elixirs, gear or other useful items. Item drop wise, increase drop frequency of actually good items makes a lot of sense, as they cannot be traded it's not like it would greatly impact the general market.
Making achievements account based instead of character based seems like a good idea, it seems impossible for a HC toon to make it on the top of the LBs so making the achievement account based as well as titles would provide more incentive to do hardcore. Perhaps also unique vanity outfits or gem rewards for HC based achievements that can are automatically rewarded into stash, cannot be traded, but then also give an endgame use for HC mode.

In general I think hardcore would be interesting and a fun challenge, however I think it would make more sense to have specified content or system for those character as opposed to just have general rules and throwing them into the same content.