More specifically, is it a goal to make Linux match up to the Single UNIX Specification?
Additional details would be nice, for example.
The truth is Linux does not need SUS certification and does not want to become Unix. And it doesn't lack in anything by doing so.
You need to pay in order to become SUS-certified, and it's actually very expensive. This is what BSD-like and GNU/Linux operating system vendors don't apply to it.
Most of all the GNU/Linux distribution follows the Linux Standard Base, that is free of charge and recognized by almost all the Linux vendors.
No. If anything, in practice UNIX(tm) systems have been becoming more and more GNU/Linux with time. Some in look and API, most by actually offering ports of GNU software for their system.
Most importantly, Linux is just the kernel and there's a crazy number of "operating systems" built with it. Some of them might indeed be interested in pursuing a certification, but it would probably not be worth the effort. Most wouldn't want to be bound by any antiquated spec anyway.
The LSB is a more open effort and many will happily break even that to follow their own ideas.