Why use a descriptive phrase rather than an X to close a pop-up?

Question

On several sites, I’ve noticed a type of email subscription modal pop-up message that can’t be closed by clicking an “X” in the corner, but instead requires clicking on a sentence that describes what you’re refusing.

Here’s an example from the Cooks Illustrated website:

To close the dialog, you have to click "No thanks, I'm not interested in free recipes". I was wondering what difference it makes to user experience (have any studies shown that it has benefits?).

I would guess an "X" and a descriptive sentence compare something like the following:

• “X” in corner: users can find and click it more quickly
  CON: as a result, some people who would like to subscribe might close the popup before realizing what they're refusing. Fewer people subscribe than with a descriptive sentence

• Descriptive sentence: takes longer to process
  CON: as a result, people might get annoyed by it and leave the site

In other words, I’m thinking there is some kind of trade-off (based on my own reaction of annoyance to these types of pop-ups). But maybe the “annoyance” effect is actually negligible. That would explain why people use them, in any case. (Or maybe there is some negative effect on UX, but still a net gain in profitability.)

What evidence is there about the effects of these two ways to close a modal email subscription popup?

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^{(I read a related question "Is it necessary placing exit/cancel/close button if there are 'x' (close button) at the pop up window" that mentions a third pattern, having both descriptive text to click and an "X", but I don't think that's so relevant here. If you know of any advantages this has over the other two options, please explain!)}

Answer 1

Such a method of closing makes the user look at the popup for a longer while as they actually have to read through it to find how to close it. This means that a user is more likely to actually take an action from the popup. Also, writing something like No thanks, I prefer to waste my time searching [for something] will once again make the viewer think about whether they shouldn't take the required action like entering their email.

Answer 2

Some reasons include the fact that some may not notice the 'X' in the first place or be unsure what it means or that it even does anything. Even today some people are unsure of what the hamburger menu is. Don't give too much credit to the general population.

The "No" phrase is a chance to encourage a visitor to still take a positive action. Personally, I find the phrase used in many of these cases insulting.