> If you voluntarily walk into someones shop [business], can you demand that the shop owner doesn't catalog that event?
No. Rather, the GDPR allows the shop owner to ignore such a request (that "someone" walked into the shop).
If you purchase something, and they keep records for invoicing/tax purposes, your request for erasure of that information can also be ignored.
> If you voluntarily agree to receive access to a service in exchange for data collection, can that legal contract be invalidated by decree?
No. However, you do have a right to ask the service to stop processing your personal data even though this may prevent you from accessing that service in the future.
> you can't stop people from voluntarily submitting their data in exchange for services - there is simply no legal theory in support of banning that.
And the GDPR doesn't do this. Indeed, I can offer a £5 amazon gift-card in exchange for some personal data that I will share with my client, and provided I'm overt at the time of the collection, and I hand over the data immediately (i.e. do not keep a copy for other uses) there's nothing the data subject can do to screw me out of what's a perfectly reasonable deal. Their right to erasure is irrelevant since I'm not keeping the data; they have no right to stop processing because I'm already done processing. And so on.