By adding HTML5 video and now its DRM-related infrastructure, WebGL, and other features that developers used to use Flash/Java for, you are also increasing the attack surface of the browser "package" as a whole. The comparison is a perfectly reasonable one.
Unless more than one browser uses, say, the same video codecs, or the same third-party DRM-related module, or the same system services for doing hardware-accelerated 3D rendering.
There may be some marginal advantage to having different implementations in different browsers, but marginal is probably all it is. Realistically, as things we used to do in the likes of Flash or Java move into browser-native implementations, there is still no reason to assume that the people writing those implementations will magically produce completely secure implementations where no-one ever has before.
But your main point is a very good one. There are way too many people in the industry right now complaining about those older technologies who think that the world somehow magically owes them updates to 10-20 years of past work, just because their bleeding edge browser-native tools have finally reached the point in the very recent past when they can do some of the same work to a useful degree.
There are also way too many people moaning about how these plug-ins are such horrendous security problems while ignoring the facts that (a) every major browser also has a less than stellar track record on security issues, with Firefox and Chrome patching numerous vulnerabilities in updates every few weeks, and (b) moving the more advanced, and often hardware-accelerated, functionality from plug-ins to native browser capabilities isn't really reducing the area of the attack surface, it's just reshaping it. Given these facts, there is little reason to assume that browsers will inherently be more secure just because plug-ins were forced out in favour of native technologies. As others have been pointing out today, the reverse might actually be true, because at least the plug-ins have a degree of isolation and click-to-play safeguards are now widespread, while the trend with browsers (again, particularly Firefox and Chrome) is to remove obvious settings that would allow users to turn off certain functions.