In New York the website recently updated to do this, presumably because they were forced to. They had a whole banner announcing it.
I'm Australian and moved to New York recently-ish. It was one of those classic anti-consumer disappointments one experiences moving to the states. Glad they fixed it.
That's one thing, annoying but possible to work with.
What I'm talking about is Dynamic Pricing. Had to look up what really happens: The host sets a rate-range, and Airbnb first gives the low price and then as you click around in the area they notice you're more interested so they increase it towards the high end of the price range (possibly also time of day and such signals?). Then I guess there's a slow cooldown.
Like how a good haggle is made to give you a friendly relationship with the seller, this seems specifically designed to make people hate Airbnb and swear to never use it again.