Marketing teams are usually data driven rather than user experience driven.

How does one counter the argument that "anecdotal evidence suggests people who sign up with us are 2x more likely to convert, so let's force more sign ups to increase revenue".

Do these people ever consider that they might have their causation backwards?

Of course, and this does get pointed out to them.

But it's easier for them to extrapolate data and say, hey, we couldn't get emails of xxx thousand users, so we lost xxx amount, vs our argument that they probably lost a number of users who were annoyed by the popup.

Except, you can count conversions, but you can't "measure annoyance"

For many the reason is Facebook who canibalized the brands natural reach without paying.

Everyone panicked and good old email is trustworthy. FB holds the contacts in their paid garden that they once so hard fought for.

That's more so they can bring you back even if you weren't actively looking for something ("wow, widget x is 50% off - I'll probably need it in the next few months, I should buy it now."). Also to keep their brand in the front of your mind the next time you do actively look for something.