Hi—I love to use Sketchfab in order to be able to showcase my work fast and easy to people who don't necessarily know what 3D work entails. It's really great for that purpose. However, while all the graphical bells and whistles work great on a computer, they don't always behave nicely on a phone, ESPECIALLY for animated content.
For example, this model of mine performs decently enough on my Galaxy S7... but it's quite jittery in its performance, which is unfortunate when animated:
What might be interesting is being able to disable certain things on mobile. It could be in the player, sure, and in a way, we already have that through the model inspector, but that disables ALL post-processing effects. And my model up there really benefits from the tonemapping, for example—but it could still look great on mobile without bloom and dynamic shadows.
For example, tagging post effects or material effects as "don't enable this on mobile", e.g. subsurface scattering, bloom, SSAO. Same for the "enable shadows" flag on lights.
VR already force disables certain things for the sake of performance, but I would argue it's a special case; when it comes to mobile, offering fine-grained control of what you know you can disable and get away with it would be great.
But sometimes your model is just too detailed, and being able to specify a lower-detailed mesh for mobile might be nice... but I'm sure that's a feature that would get complicated real fast. That said, I'm sure it would really benefit people who want to share photogrammetry and 3D scans.
It might also be cool to have some kind of performance visualizer tool that tells us what is the most expensive thing in our scene—perhaps as part of the model inspector panel... though it is true that this seldom changes when it comes to mobile phones: it's probably going to be 1) vert count 2) dynamic shadows 3) bloom, from what I understand.