I was playing around with Moqui last friday, and I figured out how to make Moqui a Progressive Web App. You can check out the diff for it here. This is mostly just a proof of concept, and would require more work (configurable images, metadata, etc.) before merging into upstream.
If you want to try it out, run moqui with the diff applied above. This is based on this article which explains how PWAs work. Then test using google’s lighthouse which is built into the dev tools on chromium.