Better than plugins
EME is better than the alternatives.
The alternatives are:
1) Plugins such as Flash, Silverlight, etc. Currently in common use for DRM video playback. To be useful, a plugin has to include not just the DRM bit, but also the media download, video & audio decoders, and a UI framework, and a scripting language to write the video player in (for fast forward, rewind, volume, etc). Because they end up including a whole scripting language and UI framework, which have to be massive to be useful, they have a massive attack surface and are full of bugs. They also have limited availability - e.g. Flash on Linux wasn't available for a long time.
3) Something browser-specific. That gets you direct to "this site only works with Microsoft Edge". No-one wants this.
4) Streaming video sites stop serving PCs. If you want to watch Amazon Prime, go buy an Amazon Fire TV or an Amazon tablet. No-one wants this.
5) The magic fairies ride in on their flying Unicorns and persuade Hollywood to make their content available without DRM. This is the one that anti-DRM people want, but the problem is that ... unicorns aren't real, and no-one has yet found a way to persuade Hollywood to do that. Some anti-DRM people seem to believe that they can say "the web doesn't support DRM for videos" and that will force Hollywood to go "ah well, in that case we'll make our videos available DRM-free". In fact, of course, Hollywood will say "That's not true, we've been doing DRM video on the web for years - see option 1. But if you want to break that in your browsers then we'll stop supporting them, and advise people to use different browsers or Fire TV or iPads or whatever, and most people will, because in the real world most people care more about actually seeing videos than care about your ideological anti-DRM stuff." Therefore this approach would be suicidal for any browser vendor - even Mozilla realised that and added support for EME.
(Note that I'm not taking a position on whether DRM is "good" or "bad"; I'm taking the position that in the real world DRM is here to stay and there's nothing we can do about that, so lets make the best we can).