I wish there was a search engine that lets me filter and see only those sites that do NOT shove popovers in my face. I would use that search engine exclusively. Blocking visitors with popovers is a horrible practice. There is no equivalent in the brick-and-mortar world. Imagine you were shopping at Macy's or Home Depot and every time you arrive, or you cross into another section of the store, an employee steps in front of you and demands your attention. They intentionally block your access and prevent you from doing anything until you perform a magic dance or sing a specific song. It takes little imagination to see how that would end.
I use multiple ad blocker plugins and still can't stop the popovers. I have stopped visiting sites that shove popovers at me. I've removed them from my bookmarks. All of them are hawking commodity content. It's all available from their competitors. The only "value add" they can offer is improving my customer/visitor experience. So it's strange that they choose to do the exact opposite.