Proprietary drivers are shipped with many distributions. For example nvidia drivers are shipped with Ubuntu. If the repo drivers don't suit you, you can (just like on all other platforms) download drivers from the vendors website.
Proprietary drivers are allowed and are shipped in many distros (just like in Android), but they cannot be included in the kernel upstream (then they wouldn't be proprietary).
Every vendor is welcome and encouraged to submit their driver to the upstream linux kernel project. Some vendors do however chose not to do so, for a variety of terrible-to-mediocre reasons.