Browser vendors don't have to implement any DRM scheme, but they will and sites will use them. What this means in practice is that there will be 100% standards compliant, pure HTML5 websites that can only legally be rendered in specific, proprietary browsers. The
stated purpose of HTML5 EME is to make it a criminal offence under the DMCA anti-circumvention clause to develop an unauthorised browser or extension that displays the protected content.
If anything this is worse than proprietary plugins because those used documented APIs that any browser could support, whereas this is integrated into the web browser itself.