The reason the price is increasing is complex because it's a global market. Broadly, there is a new found enthusiasm for this thing that's been in a rut for months. Read the headlines on Coindesk and you'll start to get the pulse for the market.
Bitcoin is slowly gaining popularity that's why the price keeps increasing year-to-year. There's always interest on it, even though its been in a rut for months. And you don't need to go to Coindesk or any other crypto media outlet, just look at the price and you will see that's is gaining grounds again (although the we have a price correction.)
if all bitcoins were mined it will be considered totally rare because the supply will end but the people who demand on it will continuously increase and as time passes by, the price of bitcoin may become unimaginably expensive. But I don't believe that is the only road where bitcoin goes because if we remember there are also some other factors that could affect the price of bitcoin. What I really want for bitcoin is to become stable though.
I think scarce, is the appropriate word. However, I'm sorry to burst the bubble to you that bitcoin will not be
stable because the market is base on speculation. So the price will keep fluctuating whether you like it or not.