But, as you say, that's different from running a local application. While some heavy-duty multimedia still benefits from running an app locally, that ship has mostly sailed with office suite software. I still have LibreOffice installed on most of my systems, but even if I'm not collaborating on a document, it's incredibly useful to have docs that are "just there" and I can access from any device--even including my phone in a pinch.
https://www.libreoffice.org/download/libreoffice-online/
The former LibreOffice development team from SUSE joined Collabora in September 2013 forming the subsidiary Collabora Productivity.
I hope Webasm enable porting at least some of the rendering code to client-side in the future.
What I think would really make LO stand out is strong collaboration support in the existing desktop editors. A self-hostable headless sync backend that streams real-time changes from and to everyone who has the document open would be even better than GDocs, which is notoriously slow due to being all in a browser.