I suspect it will be politically difficult to outright ban the ad model... might the same effect be achieved however by enforcing strict online advertising requirements & making websites (specifically the owner of the domain name used to access the site?) liable for all ads that they host as well as liable for all data gathering activities that drive those ads? Ideally with a requirement that all ads shown must contain a link to information about all parties involved in producing the ad & any profiling used to determine whether or not to show it to the user viewing it.

So if any ad is shown based on user profiling from data gathered illegally (i.e. without a proper opt-in as per GDPR etc) then the site showing the ad could potentially be sued?

Essentially, make it so onerous to legally advertise without risking a large class action lawsuit that the practice more or less dies out without technically being "banned" per se...