The effect that I’m assuming is that this will work until people realize it’s happening. At that point, the price sensitivity will increase as a matter of opposition to price gouging.
Price discrimination happens all the time currently, already, and has forever. Whether you know it is happening or not, everyone is still going to have a different price they are willing to pay; sure, maybe people will, as a whole, care more about not paying more in the future, but how much they care will still vary between people, and that will be priced in.