My personal belief is that most people that use the Shield as a Plex server are streaming content to devices that don't require transcoding, or only needs the audio transcoded. Things like other Android based boxes, Blu Ray players, or even some TVs. And their content is possibly in a better format for those players. For the Roku, you have a limited amount of codec and container support, so many more videos require transcoding. For example, there are a number of Blu Rays that use VC-1 video, which isn't supported by Roku so needs transcoding. Roku devices also only support a small number of containers, although as long as the codecs are supported the server only needs to "transmux" the video into a new container. This doesn't take a lot of power either but still might be reaching the limits of the Shield, especially the older models.
You mentioned everything is connected via Ethernet. Remember that the Shield has a Gigabit Ethernet connector, but no Roku device does. Roku has a limit of about 90 Mbps on a wired connection, and some 1080 content can bump into that, and 4K content absolutely does. My Ultra 4800 will connect wirelessly at about 225 Mbps, so that appears to be a hardware limit for Roku devices. Of course, that's more than even for even the highest bitrate UHD rips I have. But I still use my Shield for playback, since it supports bitstreaming the lossless audio (including Atmos/DTS:X) and will also display image based captions.
And that's one other item to note. Virtually all DVD/BD discs use image based captions, which Roku devices cannot display. So if you've enabled captions, the server has to "bu-rn" (can't believe the forum is prohibiting that word) the captions into the video stream. That takes as much power as transcoding the video, so that could be another reason the Roku is getting stuck at 33% load.