I started writing a reply and realized your question was harder than it first looked when it comes to companies like Twitter versus a service like AWS.
Short Answer: AWS provides a agnostic service focused on utilization with no specific purposes in mind, hence a metered system makes perfect sense. Twitter only exists with user driven content and needs a constant pipeline of the stuff to survive, and because the web application is free in order to eliminate barrier to entry, implementing a metered system for developers would remove incentives to build new applications because they're having to pay to compete with something people can get for free.
Long Answer: You can easily explain why a metered system works for a company like AWS because you're renting a agnostic hardware platform you can do anything on from building the next Twitter to serving cat videos to grandmom's mobile device. In this case, they can consider all usage and bits equal and charge accordingly. It gets murkier when you look at companies like Twitter or Facebook that are trying to be content companies and global platforms at the same time. These kinds of companies make money by getting users to post content to their service, letting them sell targeted ads, compiling user profiles they can sell / reuse, and by selling content to third-parties who can analyze (i.e. Salesforce purchasing access to the entire Twitter firehose). Subsequently, most consumer oriented development on these platforms focuses on the posting and accessing of content and, in many cases, consists of standalone applications ranging from open source to paid for with a couple SaSS platforms thrown in for good measure. Monetizing this ecosystem poses two separate challenges. First, the external applications hide user data from the content company. Coming through an application, the app can send the bare minimum necessary for an HTTPS connection to the API and the company won't know if the user's on a mobile device or computer, what O/S and version they're running, the actual time of the interaction (for instance, sending a delayed tweet) and a whole host of other user metrics. This decrease in information hurts Twitter's ability to build user profiles and vector the user to things they might pay for. By tightening their grip on the third-party ecosystem, Twitter ensures the flow of information necessary to keep building these profiles.
Secondly, creating a metered usage system for a content company would flip the revenue system, developers would be subsidizing users using the content platform unless they send users a monthly bill for their usage of the app. This would completely destroy any third-party ecosystem since the web app is free. Why pay a monthly bill to use a otherwise free service? Sure, you might see some adoption, but I would argue it'd be microscopic compared to an ecosystem built on a free API.