[madmax2]

I think it depends on your definition of 'smooth'.  AIUI this device is still stuck at permanent 60Hz output - so any 24fps content will have 3:2 pull-down added, and any European 25/50Hz stuff will be even worse.

(I think unlike other Chromecast stuff it doesn't even allow the option of permanent 50Hz output?)

-AIUI this device is still stuck at permanent 60Hz output - so any 24fps content will have 3:2 pull-down added, and any European 25/50Hz stuff will be even worse.
I have no idea by what you mean by this... please clarify what actually happens (or show me a video or screenshot that has these issues) when the video is playing with 3:2 pull-down added..

Movies and most US scripted drama and comedy is shot at 23.976/24fps. To display this on broadcast TV in territories that have 59.94Hz TV (like North America, Japan, Korea etc.) you have to convert the 24fps to 60fps (*) and the standard way of doing this is 3:2 pull-down - which display one frame 3x, and the next frame just 2x. This asymmetry makes any linear motion judder. If you grew up watching it you may not notice it, but many do (particularly those of us in Europe who didn't see this much growing up). Some TVs can attempt to remove this by detecting 3:2 and removing it. However the best route to avoiding this 3:2 motion judder is to output 24fps video at 24Hz, then your TV can display this at 48Hz, 72Hz, 120Hz, 240Hz etc. by showing each frame 2x, 3x, 4x, 5x, 10x etc. This means every frame is shown an equal amount of time and you have no judder.

Devices like the Apple TV, Amazon Fire Stick (**), NVIDIA Shield TV (**) and most LibreElec/CoreElec platforms can be configured to output 24/23.976fps stuff at 24/23.976Hz, 25/50fps stuff at 50Hz and 29.97/59.94Hz at 59.94Hz. This ensures no judder.

The Google Chromecast with Google TV is - or certainly was last time I checked - only capable of a fixed 59.94Hz output - so you get no option to playback content at the best frame rate for the content being played.

That fails my definition of smooth.

What is "3:2 pull-down added" and what is it mean "European 25/50Hz stuff will be even worse."

3:2 added is explained above (it's what you have to do to play 24Hz content at 60Hz (*) )

European TV content is shot at 25/50Hz - if you watch any European TV shows they will be either 25 or 50Hz releases usually. Playing this stuff at 59.94Hz means some frames are repeated, some aren't. On 50Hz native content you get 10Hz judder as one in every 5 frames is shown 2x. If you see that judder, you hate it. I do.

This too fails my definition of smooth.

I just watch movies and TV shows.. 
There's only a few movies that I watch in 4k (some are also in imax resolution) .. 
not sure what Hz they are or if they are 24fps or not.. 

If you grew up in North America and only watch North American content - you might be fine with 3:2 judder, and not be watching 25/50Hz European stuff.

If you are in Europe and grew up not watching 3:2, and want to watch 25/50Hz stuff in quality, then you may find the motion artefacts introduced by the Chromecast not nice to watch.

-I think it depends on your definition of 'smooth'.
I mean smoothly as in
-watchable video, that does not stutter, have artefacts (or any video image issues), audio issues (out of sync, no audio etc), no black screen.. etc. and anything else that would deem the video is unwatchable even if it can play the video..
Essentially like being able to watch a 1080p video/movie completely on any mediaplayers that can playback 1080p properly.

Note: I have now clarify it as watchable video, not playable video, since playable video can have video or audio issues, which means you wouldn't want to watch it anyway, due to it ruining the experience.

Also is there some bug/issue if we play 4k HDR files on 1080p (no HDR) TV or 4k (no HDR) TV?

In a nutshell is this device capable of outputting a watchable 4k 10bit HEVC HDR or not or I should consider another device like nvidia shield pro, odroid n2+, firetv 4k max etc?

Do you think long term wise which would be better buy, odroid N2+ or nvidia shield pro ?

I would chose either the N2+ or the NVIDIA Shield TV. The former is just a nice CoreElec experience, the latter gives you DRM support for Netflix, Prime, Disney etc. in UHD HDR.

I have all three devices. I never use the Chromecast.

Thanks for detail explanation.
Can you list all the devices you owned?

So you actually tested 4k 10 bit HEVC HDR on your own google chromecast with Google TV, and it was playable but had the judder, 3:2 pulldown issue?

I forgot mention some other alternative devices...e.g. HTPC

What do you think of going back to HTPC build?

At least we know that it will continue to have Kodi updates (since there will always be a windows or linux kodi releases etc.)
vs Nvidia shield, odroid etc.. which may stop getting updates after a few years..
Also with a decent HTPC build, it will last longer (and be more powerful) than a nvidia shield pro, odroid N2+ etc...
You can also upgrade your HTPC if you need to e.g. more ram, more storage, better CPU or GPU etc.

There's no incentives for Nvidia or odroid etc to keep supporting their own devices forever, since they would want you to buyer their newer models..
or the devices is just too old/weak and the update would just slow it down anyway..

e.g. pi3b+ (no longer has hardware acceleration on kodi 19).