Isn't this what the Apple News+ service offers? I haven't used it, but for US $13 per month Apple says it offers content from over 400 publications. Of course it necessitates using one of the Apple OS platforms, and I've heard both good and bad about the overall design and presentation of the content, but it seems like this kind of service is akin to what you describe.

I'd think this kind of broad offering would appeal to readers more than a single-site subscription. The Apple cost of $13 per month sounds much better than, say, the NY Times cost of $25 every four weeks, but maybe the Apple access to publications is limited or has other problematic attributes.