I understand they know where I shopped, that is clear on my statement each month. But they don't know what I bought, unless I shop at a store that only sells one thing.

Many POS terminals send full purchase information back to the cc processor. This is used in fraud detection and also sold as part of your profile.

A while back Mastercard did a commercial where they showed you how you could see what you bought in your online statements.

It looks like this is called "Level 3 data" and primarily for corporate cards, not standard consumer credit cards. I'm not sure if that data is still collected for consumer purchases - I've never been offered any opportunity to see more detail about what I purchased, even for a price.

One significant benefit of having that data would be that it would be easier to remember and prove things you owned for insurance purposes after a loss.