One of the reasons this is important to me is because of the resource consumption of Electron apps.
I feel that having PWA support would make Orion a usable alternative to Electron apps. A particular feature I would like is enabling "Low Battery Mode" specifically for the progressive web apps (separate from the main browser).
What would be really amazing is if we could enable some of these UI changes for normal sites, even if they've chosen not to support PWA (like Discord).
I've made a more specific proposal in a separate issue, to have "isolated background sites" (Or: Progressive Web Apps for all)