A user from Twitter reports that purchased content doesn't prompt to install Widevine.
Widevine currently only prompts to install based on URL pattern:
https://github.com/brave/brave-core/blob/a57dc16dba02ea52adcca39a5189533e15168752/common/shield_exceptions.cc#L127
But we don't want to prompt for all of youtube.com for Widevine.
So we'd need a content script or some kind of network filter or other detection mechanism.
If Widevine is already installed, it does play.
I haven't tried these steps yet, but I think they would be:
Video doesn't play

It prompts to install Widevine in the URL bar. Clicking the prompt should make the video play.
Always, as long as Widevine is not installed.
There is also an issue on Spotify & Amazon.de where users don't get prompt for Widevine to play prime videos, but works on primevideo.com
+1 from Community for amazon.de https://community.brave.com/t/are-there-any-solutions-for-widevinecdm-problem/37966?u=eljuno
+1 here too
Verification PASSED on macOS 10.14.2 x64 using the following build:
Brave | 0.59.28 Chromium: 72.0.3626.64聽(Official Build)聽beta(64-bit)
-- | --
Revision | eaa9668e80ce5405e7f1902579558ea725c06ca1-refs/branch-heads/3626@{#708}
OS | Mac OS X
Netflix, YouTube and Amazon Prime VideoAmazon Prime Video -- PASSED

Netflix -- PASSED

YouTube -- PASSED

Verification passed on
Brave | 0.59.28 Chromium: 72.0.3626.64聽(Official Build)聽beta(64-bit)
-- | --
Revision | eaa9668e80ce5405e7f1902579558ea725c06ca1-refs/branch-heads/3626@{#708}
OS | Windows
[PASS] Amazon Prime Video

[PASS] Netflix

[PASS] youtube

Marking issue as Windows/macOS only as Linux doesn't support Widevine (yet)
Most helpful comment
Marking issue as Windows/macOS only as Linux doesn't support Widevine (yet)