Is it really more profitable

It is. Online, you can use statistics and probability theory to actually test what's more profitable instead of relying on ad-hoc metrics about what "feels good".

They chase you around the web, even for products you already decided you didn’t want

These are a small minority of online ads. They're displayed in places where nothing more profitable or contextual can be displayed. (I.e., most websites, since most websites are junk.)