Never mind Audible (is this still working smoothly on Windows?), there are plenty of public domain audio books and also plenty of third party applications to listen to them - even on Windows 10 Mobile. I reviewed Audiobooked UWP a while ago - and now here's Booxio UWP, small, simple and 100% free.
Minimalist from the start, this may be just what you wanted - after all, it's all about the audio, isn't it? Here's Booxio UWP in action on my Lumia 950:
Audio books in any of these formats are auto-scanned in \Music\Audiobooks on your Windows 10 Mobile phone, but you can also add specific files from other locations with the '+' control. Each book is shown with duration and current % progress.
Though the rest of the UI is minimalist, the player is comprehensive, with graphical effects, a responsive UI, skip controls, a bookmark facility, sleep timer and speed control (in increments of 0.05x); (right) books with multiple chapters (separate MP3s) are broken down sensibly here, even though they're amalgamated on the main Library pane.
All rather well done for a piece of outright freeware. Recommended for any phone with Windows 10 Mobile.
As in the original Audiobooked UWP review, the biggest FAQ by far is how do you get hold of free audio books online? There are, in fact, dozens of good sites/sources, but use this guide as a starting point. These apps and books aren't a wholesale replacement for Audible, since the latter has all the latest and heavily copyrighted content, but if you have amassed (or are amassing) a library/archive of more legally copy-able (i.e. DRM-free) audio then Audiobooked or Booxio here are terrific players.