Bitcoin is just as useful at $1/btc as it is at $10 or $100. It does the same job.
Speculators and investors believe that the value of the coins will go up when the reward is halved due to basic supply and demand. If we assume that demand continues to increase as the Bitcoin economy grows (more merchants, more users), however the rate of increased supply is decreased by 50%, the delta between supply and demand will widen. When demand outpaces supply, value goes up.
The difficulty to mine blocks is irrelevant as it is self-regulating and will always average out to one new block roughly every 10 minutes, which keeps the rate of supply steady. What will be changing is the AMOUNT of supply provided at that consistent rate.