My biggest issue with modals, is that they never seem to be tested with mobile devices in mind.
So when I'm on my phone, the ability to close it is often off the screen.
The only choice is to leave the website at that point.
So the only logical thing to do is avoid the site in the future, they're more interested in extracting money from their existing readers than getting new readers. Sorry, maybe if you had let me read one article I may have liked your content.
I feel your pain.
The web sites I maintain have at least 70% mobile users. But the managers (and designers!) only see them on giant-screen desktops, and only care what it looks like in-house, not to the customers.
I'm tired of constantly telling layers of bosses that what they want won't work on mobile, which is where their customers are.