It would be good if EPiServer could make some changes to support Progressive Web Applications (PWAs) as this is the direction that a lot of web applicaitons are heading. To do this I think the main issue would be to support native ajax rendering of blocks for a page in the CMS. Also possibly generation of the manifest from data in the CMS (like screen sizes, etc) would be good but not essential.
What issues are you having?
As I see it you can today generate the manifest form data and load page or block data via ajax.
The main issue is that loading block data via ajax is not in included by default and for progressive web apps this would be the default as they all use web components and there would only ever be one page most of the time. all other HTML content is in the web components which would be blocks in EPiServer and rendering blocks through ajax still feels like a second class citizen even with partial routers. An I'm not sure that partial routers really meet the need of ajax rendering and seems overly complicated to setup if this is the focus of your site.
I also like this scheme of How Progressive Web Apps work
For those that come accross this thread EPiServer have done a demo app using vue.