Bitcoin price should stabilize if there are more transactions.
Biggest issues now are slow payment time, hoarders and over-reliance on few exchanges. I think higher price and faster payment/withdrawal times would decrease the price eventually as bitcoin holders would have more incentive to spend/take profit while the price is high and exchanges would be forced to sell coins after a transaction for merchant withdrawals. For hoarding, if protocol can be updated to charge higher transaction fee for long-held coins, this should make it less profitable to hoard and increase number of transactions.