EME should be a permissions, just as much as asking for the users microphone and web-camera. Iirc when Firefox caved in on this whole CDM thing, they made it something the website needs to request access to before it can be activated.
I see no technical reasons for why Chrome shouldn't be able to do the same.
I guess Google has an active interest in promoting DRM, and as such making DRM cumbersome to use is counter to that goal.
This is actually the case, but the setting in incomplete, you have a setting called "Allow sites to play protected content (recommended)" in the Settings (Chrome 57).
I see no technical reasons for why Chrome shouldn't be able to do the same.
I guess Google has an active interest in promoting DRM, and as such making DRM cumbersome to use is counter to that goal.