Let's just make forks of Chromium and Firefox that include built-in support for as many codecs and file formats as possible. Someone wants to use a psd in an img tag? Sure! Someone wants to use a flac in an audio tag? Go for it! Want to use a bink video in a video tag? Be my guest.
Even if it's illegal, who cares. You can do it the same way that Windows Media Player and Ubuntu handle it. Every time the user comes across a video they can't play, a popup asks them to click a few times, and then voila! They have the codec.
Web developer are always going to have a crappy time of it. We will never ever be able to simply make one site one way and have it work nicely on all devices with web browsers. Give up on that dream. But the dream of making things good for the users, is achievable. Aim for that first.