A site is much more like a shop - private property, but a public place, and therefore it has legal restrictions if you want it open to the public.

Even if that argument holds, and I want to analyze which sections of my shop or store are frequently visited, how often users buy goods, and effects of various changes that I make, I don't see why that should be illegal except in cases where I actually ask permission from every customer who walks into my shop.

This doesn't prevent you from analyzing which sections of your shop or store are frequently visited or how often users buy goods - that can be analyzed using the server logs.

Now, should e.g. Wal-Mart be able to put an RFID tag on you so that they know who you ware the next time you come in? And more importantly, should they be able to contract a third-party, which can then know when you enter any store with which they have a contract?

And shops do his there is an entire specialisation in market reaserch in doing footfall analysis ie where people walk in shops why do you think they know to put sweets next to the checkout in supermarkets.

Sure, but I still need to know where you are and what you're doing in the "shop" to make sure you're not just making it crap for everyone else