Not necessarily browser plugins. Could be browser or OS or hardware.. Each website has control over what DRM it accepts, which leads to a world where hardware eventually becomes the requirement.
Regardless if it's technically a plugin or part of the OS accessed through a bridge, or anything else, EME fundamentally depends on proprietary code (and that code will not be part of any open source browser).
Then it would only be a matter of hacking one browser to claim to support drm scheme x and then not to get it to work. Since we have to distribute the run time in at least one browser, this shouldn't be a problem.