I would be very worried about customers finding out that other people in the same country got offered different prices. Here's an example of a story from the Atlantic[1] that describes it in a very poor light. Making sure someone always gets the same price on refresh doesn't hold up if they are browsing at a friends house for example. I would be very worried about getting shunned for price discrimination.
[1]: https://www.theatlantic.com/magazine/archive/2017/05/how-onl...