I agree that it is way too difficult to manage a bunch of monthly subscriptions, and also that having to put my credit card information into a website (and have it bill me every month) is basically as bad if not worse as putting up with the advertisements on a website. However, I think that micropayments/a flattr-style fund for reading articles is doomed to fail because of the psychological shift between "I'm reading this article for free" and "I'm reading this article for $0.01, I only have 1000 of these left this month, maybe this isn't the one I really want to spend this on." My opinion is that a Spotify/Netflix-style subscription model is the best: collect subscription money, then pay per-user that accesses an article. However, the issue with this model is that the "network" of things that you are allowed to read will be really small at first.
That said, here is my proposed business model. Create an app that allows users to load money into the app monthly and issues each user a unique credit card number[1] for subscriptions to other websites, giving a central location to manage subscriptions. Once you build up a number of users on a single site, go to that site and say "Hey, you can save the 1% of the subscription cost from our users that's eaten up by credit card fees[2] by going through us to manage subscriptions. Oh, and it will also increase your conversion rate among our users since it will only take two clicks to subscribe instead of having to enter a bunch of credit card information. Once you have a critical mass, you go around to companies and now create the Netflix-style subscription service. If you're clever, you probably can create article-level bundles, e.g. "every article in our network that was linked to off of Hacker News," but NOW you have the pay-to-read subscription with a critical mass of information that people want to read, instead of "we're launching with these twenty sites from these four companies and we hope to add more."
[1] Yes, there are a bunch of problems with issuing credit card numbers. Yes, I know I complained about having to enter credit card numbers in the first paragraph. This is a big picture thing.
[2] This is kind of wrong, since a credit card fee will be charged to load money into the app, as well as for disbursements. At this point, the startup would probably have to eat that fee or heavily push ACH/lower fee methods of payment (even though I hate companies that push ACH for this reason).