I still have no real idea what the .a stuff is all about. If it helps so much, why default it to off? What is it buying you to not have it.
The .a is a precompiled archive of the library. To use this feature, the library author must compile the library for every target architecture. So it's not just some magical switch you turn on in library.properties. It takes effort from the library author to generate these .a files and put them in the correct folder structure, then that effort needs to be done over again on every release. It's not a huge amount of work, but many hobby developers already don't have enough time to properly maintain their projects.
Many Arduino libraries (including yours from what I can see at a glance) are non-architecture specific, so precompiling it for every architecture it could possibly be used with would be challenging.
The whole idea of supporting precompiled Arduino libraries is a bit controversial because it permits closed source libraries. Officially adding this capability to the Arduino build system was specifically prohibited for some time. However, there is a legitimate use for this feature beyond "you can use my precious library, but you're not allowed to look at the top secret code": precompiling large libraries saves a lot of time on the compilation process for sketches that use it. There is now a "precompiled=full" setting that allows providing precompiled versions for specific target architectures, but also having the builder fall back to using the source files when compiling for a board that precompiled files weren't provided for.
Even though it's unfortunate to see closed source libraries, there are some cases where this is all we have available. Some chip manufacturers have an unfortunate habit of not making their libraries open source, so you either need to work with the closed source library or nothing at all (unless you can manage some genius level reverse engineering to write your own). The precompiled feature allows the creation of "mixed source" libraries where a community member is able to create an Arduino library that wraps a closed source binary with open source code, extending the functionality or providing a more user friendly interface.
I've recently done some work to try to fully document this feature and make it a bit easier to understand. That was done after the "0.11.0" release of the documentation, so the new content is only visible when viewing the documentation with "dev" selected from the version menu:
Please let me know if you find anything in specific to be unclear.