More specifically, I'm assuming that they are a speculative instrument where people are expecting positive growth (i.e. that bitcoins become more valuable over time).

The supply of new people earning money who will want to invest income into Bitcoin has to be finite. Growth can't continue forever because you always need to find someone new who is willing to pay more than you did for a bitcoin/satoshi to keep the price growing, and there isn't an infinite supply of people with an infinite supply of money.