> Because having something priced as "free" is distorts the market.
Only if you consider the "market" to only take price into account - which is a very simplistic model that most people don't adhere to.
You pay for things with your money, time, attention, and personal information. The only problem with the current market is that, while it's extremely easy to see monetary prices (due to effective government regulation, I might add), it's far more difficult (or impossible) to see those other three "prices". Were they equally visible, there would be no problem.
> There's plenty of experiments with people having to choose between something that is $1 in price difference and when both options are paid, people make a rational choice. However, when one of the options is free and the other cost 1$, a disproportionate amount of people choose the free option.
What's happening here is just a "rounding down" of a particular cost to zero, which isn't relevant if the associated cost isn't close to zero. Specifically, if the two options are (1) pay $1 for thing and (2) pay $0 but expose your IP address to the website, the latter option will get rounded down to zero the vast majority of the time because people usually don't care about their IP address being seen. However, if the two option are (1) pay $1 for that thing and (2) pay $0 but give them your real name, mailing address, email address, phone number, and SSN, and the buyer is aware of that upfront, there will not be the same asymmetry, because that private information does not round down to zero.
The correct solution is to regulate transparency such that, alongside the "free" sticker price, consumers see a very clear warning label "you will provide your full name, email address, and phone number, and these will be sold to 17 parties[link] for advertising purposes" - in other words, actually expose the privacy cost as part of the "sticker price" alongside the monetary cost.