Not with extensions, with plug-ins, and they were already doing it. Flash and Silverlight came with DRM for any publisher that wanted to use it. Many did.
Plugins would be fine; you could always point out, that they are non-standard. Now, if you fail to support the right EME plugin, it is the browsers fault.
I know, but that's not the point. The point is, that the pain for the non-standard support had to be taken by the proponents of DRM. Now, it is up to the foss crowd.
IOW, it was not about tech issue, but about social issue / blame-shifting.