Yes, I have found out the hard way that an entire generation or two of internet users has lost the ability to visit a website to see what's there. They rely on having notifications or emails come in so that they can react to things rather than proactively go seek them out. I tend to eschew push the forms of communication, for the same reason my mobile isn't covered in a colorful grid of apps: I want to actively be choosing what I do rather than having a set of options put in front of me that I get to pick from.

But that's all just a rant. Your core point is completely correct. If you want readers, you have to cater to this 'push' mentality, I think.