You have plenty of choice: make your own, feed them wrong information, feed them no information or find a site that doesn't. If enough people care about this niche then your website would succeed.
- I cannot just make a website or service. It is usually a huge project that only few people can solve.
- I have no way to feed wrong information without diving very deep into that website's code. We are not just talking about data I enter, also about things that are collected without conscious effort on my part. It is not practical at all to feed false or no information. If they sell my IP address, how can I feed wrong or no information?
- Finding a site that does not act like this is the only way left, and it is exactly what the parent explained does not exist, because realistically, there are many topics for which virtually every site does act like this.
The rational reason for that is that in the real world, not all choices are made by perfectly rational, superhumanely intelligent actors that have and consider all the information.
Also, not all decisions on a free market are truly freely made. If all standard housing/mortgage contracts contain that you have to sign away your kidney as a security deposit in case you can't pay your rent/mortgage rates, do you really have a choice?
With data on web sites, it's the same. Almost every web site collects data. You don't realistically have the option of going to a different news site if you don't like that deal.