But, even Firefox has a rather limited UI... Whenever you build anything with a moderately complex UI, it becomes nearly impossible to offer a good cross-platform experience.

I also think that standing on the shoulders of bootstrap and material design (like materializecss) is a better place to start where users will be cross platform than trying to look native everywhere... not to mention that native looks different every other OS release. Hell, look at MS Office from version to version, they break most of their own rules. A relatively clean, usable design is more important than getting everything precisely native looking everywhere.