Definitely a way to go. Some browsers already have the "reading mode" feature which accurately distills useful content for display while the page is rendered in background. But it would be really nice if advertisers considered making ads more tolerable.
Well, calling a spade a spade... Our point is, that when you opt to receive certain content (like say, goals or runs being scored in sports) you're more likely to value a brand for providing this info than one simply spamming you with adds. It's up to the company sending you push to send you only push you want to receive, otherwise it's just spam which might make you a former customer. We only supply the tech, companies/individuals decide what to do with it.
Chances are, there is a ketnel wakelock held by a device driver and preventing the phone from sleeping. This is a common issue with poorly written drivers (even Nexus 7 3g suffers from it). Properly functioning Android phone should be managing its radios automatically.