It would probably be good to get some sort of consensus on tagging style (
pr.probability-theory vs plain
probability-theory.) I'm not sure if strict tags can / should be used and enforced on a site more visible to the public.
So for MO the prefixes are very useful because we're used to that system for the ArXiv and we know that it does a good job of top level tagging. However, it's not at all clear to me that they're useful for this site. In particular, users of this site won't typically know what those prefixes mean, and there's no reason to expect that they do a good job partitioning elementary math questions. On the other hand it might be convenient to have some similarity in tagging between MO and here so that if and when questions can be migrated directly between them we won't have to do lots of retagging...
As Noah pointed out, MO tags may not be immediately useful to this site - but we should seriously consider the long-term here and who we are... It would be nice if this site served as an incubator for future MO users, so I say we should start using the "big boy" tags now.
The status end of 2018 is that while the tagging systems of this site and MO evolved somewhat independently, eventually, the MO top-level tags with prefix (with one exception) got introduced on this site as synonyms.
Thus, everybody who wishes to use them can use them. Yet, the immediate motivation for crating them was to simplify migrations. (A migration attempt with no matching tag is rejected.)
The exception is the gm.general-mathematics tag. It is not present as synonym as it seemed not feasible to have this as a tag here. However, it still does work as regards migration.