I just confirmed that watching Netflix 5.1 content on the Streaming Stick connected to my AVR works fine. If anything, the audio might be slightly ahead of the video (opposite of the problem I had watching 5.1 content directly from the Roku TV).
You had me scared for a minute though. The way I used to test audio sync on the Roku TV was by watching "lip sync" test videos on Youtube. The Roku TV would output these in 5.1 audio even though the clips themselves were only stereo.
I was testing the same way with the Streaming Stick until today, when your comment made me realize that apparently Youtube on the streaming stick doesn't support 5.1 audio at all, it only outputs stereo PCM. That's somewhat disappointing, and it makes this problem much harder to test.
Anyway: all of this lends further evidence to my theory about what's happening here, that it's a fundamental problem with the idea of a TV playing 5.1 encoded content. There is some inherent delay (~200ms) in decoding DTS / Dolby bitstreams. Traditionally this hasn't been a problem because an external device generates the audio and video streams and sends them both to a TV or AVR via HDMI. The TV or AVR knows how much the audio stream will be delayed by this processing, so it can delay the video stream by an equivalent amount to keep the two in sync.
With these new Roku TVs that play content themselves (instead of from an external device), this paradigm isn't sustainable. The TV playing the video component of the stream has no idea how much of a delay will be introduced by the downstream AVR, so there's no way it could possibly compensate by delaying the video stream. This will simply never work, unless HDMI ARC has some sort of provision to return the AVR's internal audio delay back to the TV.
Everything you stated sounds reasonable. But, I will say that I have the TCL 55P605 with a Vizio 5.1 soundbar connected via HDMI ARC. Are there instances where the 5.1 audio of content (OTA, HBO, Amazon, etc.) may get out of synch? YES. But, that is the exception and not the rule for most 5.1 content that I stream. A few firmware updates back it was worse, but most content now is acceptable. If I start jumping around in a stream a lot there will definitely be some slippage at some point. Exiting out of app and then back in will normally allow me to stream without incident. My Vizio soundbar has an Audio Delay feature, which I can use to snap a stream back in synch while playing, but it is normally for that stream session only. One thing I did do with my Vizio soundbar setup is turn off as many post-processing features as possible. TruVolume - OFF, MUSIC or MOVIE processing - OFF and set to DIRECT. I figured I didn't need to layer any additional post-processing delays on top of what is already an issue. Perhaps it is a placebo effect, but it seems to mitigate most issues that I was seeing with audio delay.
Obviously, a solution 'fix' from Roku and TCL is what we all want.