Apple News does this. Tons of magazines across the spectrum and number of larger US newspapers. If you aren't in the US or at least wanting to read in English, I don't know.
In fact in France quite a few major French, local and some international newspapers + tech + science + entertainment + + + magazines are free online with a library registration. The service is called Cafeyn, and you could bookmark, print or save as pdf pages of all publications available.
In general HN doesn't like apple's approach to news aggregating (i.e. a closed app rather than a 'super account' that works on native websites or an RSS-type feed) but +1
I wouldn't rely on their aggregation. But, with a subscription, you can just read the magazines in the same format and layout as they are printed. No aggregation to get in the way.
