How do you propose to target ads without mining peoples' data?
Traditionally, this has been implemented with third party cookies. The retailer drops a cookie on the users browser, and then buys ads to be shown to anyone matching that cookie. I don't know if I would call this data mining, but it is certainly not private.
It is possible to build a system that supports remarketing in a private way, however, with new browser APIs: https://github.com/WICG/turtledove
(Disclosure: I work on ads at Google, speaking only for myself)
Is that something that people want?
Imagine someone wants to buy a table saw and their requirements changed and they no longer need it. It would be pretty annoying to have table saws follow them around the internet when they literally don't need them (and get in the way of other ads they would potentially be interested in).
It's also a privacy issue; if someone is searching for certain sensitive items they'd rather not have those follow them around for weeks down the line.