I think they would be a bit too strong if you could choose.
Though power creep is such that it still might not be good enough I guess.
There are so many discard cards totally unplayable so I think you would only need to rework the ones that see play right now - SoulFire/Doomguard. If you up the mana cost of each of those by (1) then it might help the whole mechanic.
I don't think it would be too strong if it just discarded your oldest cards. There would be pros and cons. You're holding 6 cards and you want to play Doomguard, but your two leftmost cards are soulfire. Puts you in an awkward situation, but at least you know you aren't gonna discard that second Doomguard you just drew.