No it isn't. Most people don't use an init system with Docker images. However, one of the top-10 popular images uses one -- the Passenger Phusion base images. They make a pretty compelling argument why you should.
None of these arguments are relevant in the big picture. Where Docker shines is the package management, not the virtualization. As a package management system, it is brilliant -- though incomplete. The package management could be fully content-addressable, and at which point, we'll have something more brilliant than what it is now. But it isn't, and I doubt anyone will try it until after this core concept gets adopted into the mainstream.
Ten years ago in 2005, I've heard these same types of arguments about cloud providers, the Zen hypervisors, and the AWS API. I've seen old mainframe folks rolling their eyes saying the technology is old, and this is hyped up. Of course it's hyped up; but unless you can look past the hype and your contempt, you won't see what's really there. No one is really arguing about cloud technology now, and the hold-outs are outnumbered by the majority.