You are entirely correct. This will eventually develop all the problems associated with a strictly limited currency. If a nation's economy was purely based on bitcoins, one would expect that economy to quickly grind to a halt as people start hoarding their bitcoins instead of investing them in businesses, etc. (BTW something like this is currently happening to the world with gold).
However, I doubt any economy will be purely based on bitcoins. If successful, the bitcoin will merely be a useful way to do painless and anonymous internet transactions, and not the only money out there. And if bitcoins get too rare for internet transactions (because people are hoarding them) it would be very easy for someone else to start another bitcoin-like currency.
If bitcoins become so valuable, this by definition means that people are offering and trading MORE goods and services to get bitcoins, not less. Prices will adjust! Trades will continue to be made. That is not what I would call an economy grinding to a halt. This is the opposite of grinding to a halt.
You do realize that bitcoins are extremely divisible, right?
You have heard of Time Preference, right? People aren't going to stop buying goods and services altogether because they believe they could buy more in the future. Sure they'll actually save more than they would with a money that loses value over time, but they still have necessities they want to buy, and toys they want to play with now rather than later, old goods that wear out, need new cars, want a new house (or another house), etc. Why do you think people want money in the first place? To live a long destitute life and maybe spend it if they don't die first?
People have used gold as money for thousands of years...how come suddenly current generations are trying to stock up on it more than previous generations? This surely couldn't have anything to do with the insane economic environment created by the various governments, their central banks, and the giant businesses practically created by those governments!?
Bitcoins will never become "too rare" for internet transactions. The protocol currently supports the total bitcoin supply being divided into 2,100,000,000,000,000 units, and that can always be changed if most bitcoin users think they need it to be divided further.
However, I doubt any economy will be purely based on bitcoins. If successful, the bitcoin will merely be a useful way to do painless and anonymous internet transactions, and not the only money out there. And if bitcoins get too rare for internet transactions (because people are hoarding them) it would be very easy for someone else to start another bitcoin-like currency.