Disclaimer: I use them and so do many of my competitors.
"Does a poor job of increasing conversions" is the opinion of someone that has never looked at the data. You can be sure that the people interested in conversions run analytics and A/B testing on everything. If these pop-ups did a poor job and there was a better alternative, you can be sure that everyone would have already migrated to that alternative.
The "rule of seven" can also be used to counter her argument. That is precisely why businesses try to get the email of visitors: to have more interactions. Otherwise, for the vast majority of visitors, the first visit would be the only interaction they will ever have.
"Works against user goals" might be true for short term goals like jumping through the most amount of content. However, users have different goals and short-term ones are often not the best goals. A pop-up might address other long-term goals the visitor cares more about than going to yet another web page.
But more than anything, these pop-ups serve business goals because most of these websites exist only thanks to their revenue. Without them my business would probably not be viable. I assume that many accept the small annoyance of a pop-up as the cost of keeping the websites they like running. And if the pop-up appears when the user is about to close the window, it does not even stop a visitor in his tracks. He can still close the window without any extra click.