A few words about "real-time engines":
Understand that even though it's a "real-time rendering engine", the render times depend on your scene. With such render engines, you can optimize your scene like a video game until it reaches 16ms/frame to render. Actually, it's not that you can. You have to work your scene for it to be renderable in real time. The same ways we make video games.
But for more complex scenes, it will take more time. It will still be insanely faster than a raytraced render like does engines like Cycles, but it might not be watchable while rendering.
And as optimizing a scene is an insane's job, most of the time you will skip that and do your renders with a few seconds/frame.
As an example, take Unreal Engine or any modern game engine: you can have actual real-time with insanely high fps (well, it's their first job anyway). But when people make movies with it, suddenly it takes more time per frame. Seconds, minutes, ... Because they free themselves from the optimization, they allow themselves to do higher quality assets and render settings, they make less use of repetitive content, etc...
Now, about EEVEE, clearly it's not finished yet, it does take a significant time even to render a still animation of the default cube. Hopefully, it will be enhanced throughout the years. Maybe this will be the base of the future interactive mode, maybe we could make actual video games in the future as we did with the Blender Game Engine. But really, "real-time engine" doesn't mean it renders in real time anything you throw at it. And when you have the possibility to make an awesome render with the only price of a few seconds of render time per frame, usually you go for it, unless you have a technical need to render dozens of frames per second.