The browser without EME will be pilloried by its users for not supporting the content they want to access. Users use a browser to access content, not to support philosophical positions on what software should and shouldn't do.
The lesser of two evils was chosen. You don't have to like it, but that's the reality of this situation. It is not realistic to suggest that the largest browser vendors not support user demanded content.
Speaking of philosophical positions, most DRMed content accessed by a user in a browser is going to be of the streaming variety, i.e. something that DRM isn't preventing you from doing something you're otherwise not supposed to be doing anyways.