It does not appear that they are exposing all possible settings configs on mobile as fallback mixing is not shown as an option for me there. This seems like an oversight to me.
Fallback Mixing is only available to Brave on desktop and Android at this time. Apologies for any confusion.
Why is it only available on Brave? Doesn't make any sense.
Because you cannot issue a cross-site request to Google from the client due to CORS policies. This feature required work in the Brave browser itself, so that the application would serve as a pipeline for the request on behalf of the search page itself.