This can't happen. If the price goes up many times due to being a store of value coin, then the quantities needed for trading or trading anonymously, go down massively because each monetary unit (1 DRK) represents a much higher value: A $100 DRK will require 1/100th of the coins being liquid and on the move, in order to facilitate trade, compared to a $1 DRK.
It's an auto-compensation mechanism.
A scarce, low-inflation, high-value coin can also be a medium of payments/commercial transactions etc. The opposite is not true however: You can have any coin as a medium of payments but not as a store of value, unless it satisfies certain criteria.
The choice is really not between
a) A store of value coin which is unable to do payments
and
b) A payment coin which cannot hold value
...it's rather
c) A coin that can do payments AND be a store of value - because these two are not mutually exclusive
vs
d) A payment coin which cannot hold value
The problem of (b/d) is this: Coin competition is strong. In order to survive out there you must have the least amount of improvable weaknesses. Every weakness of yours can be exploited by others. You can have the best technical coin and a clone will come and then say: "Darkcoin was great but it is too inflationary for it to become both a payment medium AND a store of value... so we fixed their problem and we'll do better" => problem right there.
+1 great explanation