The presence or absence of the compass rose on a VOR has no meaning.
It is purely at the discretion of the cartographer to omit it when he
feels it
would make the chart too cluttered.

All right, this makes sense to me. But as someone who is still a student, I
have to ask a question here. Let's say that I'm planning to fly along a
specific VOR radial, and that this radial is not part of an airway. What I
normally do is draw a line on the chart, and then read the radial on this
compass rose. But without the compass rose, how am I supposed to determine
the radial that I need to follow? Most of the VORs in this area have not
been adjusted to keep pace with magnetic variation, and are therefore a few
degrees off from both both the true course and the magnetic course.

I know that I can look up each VORs magnetic variation setting on
airnav.com, but what if that wasn't available?