a) I wholeheartedly want this behaviour. The phone lasts 2-3 days without recharging, and I no longer fear leaving home with 30% battery.
b) It's not an app that kills background apps. It's Android's own Background Activity Manager, where apps that are not whitelisted can't wake up the CPU. They run only when the CPU wakes up for some other reason (screen-on qualifies but it's not the only opportunity).
I had to get used to it. In one instance the alarm didn't wake me up, because it is not whitelisted to wake up the CPU. After enabling the correct apps, I maintain pretty much the same great battery life and all app functionality I want.