I agree with you. In an event of no one spending, any Bitcoin the price would stay stable for a long time. Mining would die off as there are no transactions to verify and the blockchain would freeze. Basically, everything would freeze until everyone begins to spend BTC again.
I don't think the price would stay stable for very long, a lot of people would probably start dumping their coins after a while to minimize losses. Why would anyone keep 100's or 1000's of dollars locked up in Bitcoin? All it would take would be for a few people to start selling and before you know it, the price would drop like a stone.