Not only that, but it's also wrong. Music DRM did not die. DRM on purchased music went away, but streaming music still has DRM. So the music industry didn't even completely ditch DRM like you claim it did.
Furthermore, you imply a level of informal cooperation between the browser vendors that doesn't exist. It turns into a game of prisoners dilemma, where the first person to defect gets to claim a massive feature that none of the others do, and the others are left in worse shape.
I'm no fan of DRM, but again, it's the world we live in.
And this is how it should be. I want users to get tired of installing more plugins. I want them to roll their eyes when a site says "you need to do add $x to be able to use this site." We had the same problems with mp3's, and we won out. I see no reason we can't win out with any other media.
Only if you ignore:
* Users "rolling their eyes" means nothing when they'll gladly click OK to dismiss all the security warnings and installations of n plugins so they can watch Netflix. They'll complain, but the plugin will still be installed at the end of the day. I'd rather that plugin be sandboxed.
* That the practical implications of lessened security are more real, hence important than the theoretical concerns by a sandboxed plugin who's entire mission in life is stopping you from recording a fscking video stream.
The user you're talking about, the one who signs up for Netflix, gets prompted to download a plugin, shakes their head sadly and cancels their subscription because DRM is evil, doesn't exist outside of FSF patrons.
In the music industry, DRM seemed inevitable until one morning Steve Jobs woke up on the wrong side of the bed. Then the whole thing crumbled overnight.
iTunes was not "pilloried by its users for not supporting the content they want to access". Users did prefer to buy DRM-free music, bolstering iTunes marketshare in the process. The historical record demonstrates the opposite of your hypothetical.
If Chrome or Safari drew a line in the sand and said "No DRM", that would be the end of DRM on the web. It seems they are not willing to do that. But that is a reflection on the lack of leadership at the technology companies, not on the inevitability of DRM.