Doesn't the Invidia Sheild outpt 2 channel audio form ( YouTube SiriusXM Spotify, Deezer) at the same bit rate/ resolution as the ROKU? Am I mistaken?
If you are going to use the HDMI out, then you want the audio to be passed through at its original resolution. I believe the Shield does that and Roku likely does as well. It will basically come down to which supported apps are required and which interface you prefer. Apps can vary because the Shield is Android based and the Roku uses Roku OS (Linux based).
@Trebdp83 is very knowledgeable about what formats are supported by various devices and how connecting them can affect options available.
So for your amp you need to consider how you want things connected. 2-channel amps with both HDMI in and an HDMI monitor out are very hard to find. You will have very limited options. Most people will simple choose a 7 channel AVR and just use 2 amp channels in stereo mode because it is a cheaper option. If you get an AVR with pre-amp outputs, you can use the AVR is a pre-amp only and connect the pre-amp out to a more powerful amp if needed.
The other option is to connect your sources to the TV instead and run the audio to the amp. If the amp has a monitor out and supports ARC/eARC (and the TV supports ARC), you can feed audio back via HDMI. Another option is to use the optical out on the TV and connect to the optical in on the amp or an AVR. I believe that would convert the signal to PCM or Dolby Digital. You would only need an amp with optical input like a class-D Topping or Aiyama amp. That's an economical solution.
Another option is a powered steaming device, so a streamer and amp in one unit. You don't have to spend the $3k your dealer quoted. The Bluesound Powernode is $1200 Cdn and has 80W per channel, subwoofer output and an HDMI eARC port to connect to the TV. You would need to research whether all of your streaming services are supported and whether you like the BlueOS interface (which many report favourably on) but with eARC you can also stream via the Roku through the TV to the Bluesound.