I guess the question is not if they do it, but if it is possible to be done.
Murphy's law usually holds.
Discussion
Maybe, but it's not useful. Businesses are not going to go out of their way to associate some behavior of yours to your IP if there's no name. There's zero reason to do this.
Even in ecommerce where you provide your name and address, companies never really look at that information other than for support tickets. All of the marketing is automated and insights come from aggregate data. Nobody actually knows or cares about you or what you buy.
My problem is not inherently the company setting up tracking.
It is rather the company providing tracking, the hacker who can steal information from websites, etc.
I mean of course, I could be afraid dieing as well. So my reasoning here is not be afraid of everything, but knowing the trafeoffs.
There is no best solution, only different tradeoffs.
Also I think e.g. google analytics is free.
But I guess the creation, maintanance and hosting of this service is not.
I can't imagine that they don't try to make money of it.