In standard HTML a server sends you some text bits and data streams and your browser chooses what it wants to do with them. Save them, display them on the screen, ignore them, etc. With DRM the browser has to be specifically engineered to do not what you want it to do, but what the person sending the data wants it to do. This is almost always done inside of some kind of 'black box of digital magic', be it software or hardware. If you had control or insight of the black box it is likely you could subvert control of the encrypted media.
Now I won't say that it directly enables control over your browser any more so than Flash does (Only 76 CVE's in 2014), but every black box is a point of attack for hackers.
DRM ensures that browser doesn't always behave the way you want it to behave. You no longer have full control over it, you give a part of it away to 3rd party.
https://w3c.github.io/encrypted-media/