If you want to trace the heritage of LibreOffice it goes StarOffice -> OpenOffice -> LibreOffice. All of them were primarily written in C and C++.
Under Sun/Oracle's stewardship Java was used for chunks of functionality like a database engine and some extensions. But it was criticized for it and there has been a concerted effort ever since to strip it out. I image some day it might actually happen. This isn't a slight on Java btw, it's just that LibreOffice has a larger memory footprint for stuff on the periphery and it is an obvious performance win if it can be removed.
Secondly, and emphatically, WebAssembly is not "grossly inefficient". It's a specification. It describes a binary format & assembly language and how it is packaged. Implementations are capable of compiling and caching that code and running it at near-native speeds, WAY faster and in a more integrated way than any JVM could ever. That isn't to say they *do* that at this time but that potential is there.
Also, need it be pointed out why WebAssembly exists as a thing? Look at efforts like PNaCl and asm.js to understand why all browsers have embraced it.