That's the premise that the RIAA and friends was pushing. There is of course another choice; to stream the movies without DRM. Once Flash was gone, eventually they would have caved in because there is a lot of money to be made by streaming movies.
This was a faustian bargain.
Now that DRM is in the browser, it's going to be pushed further, as with this proposal. It forced Firefox to compromise on their values of open-source in order to stay relevant. Streaming movies are still getting copied the same day.
We know from experience with the gaming and music industry that what protects the publishers is to provide a convenient platform, with reasonable prices. And of course the legal system to take down pirate websites.
And? Making people who can't help themselves from consuming DRM'd content jump trough hoops is much better than integrating this shit into the browser. Eventually media companies might have caved in and accepted DRM-free distribution like the music industry already has.
The choices were EME, Flash, or no premium VOD on the web.