I don't know how this World Cup is structured, but the way these things are usually done is that a bunch of OB trucks are hired in to cover the pitch sound -- they might be independents or from a local broadcaster, or a combination of both. Often the sound balancer will be a specialist brought in as part of a team to ensure a consistent style as will the directors and other key staff.
There is usually a coordinating centre which takes in the feeds of the pitch effects from the different venues, along with dozens of different commentary feeds, and then distributes them to the right places. It is all seriously complicated stuff with different end broadcasters often wanting different things.
Clearly, it's not ideal to try to filter out the horn noise on the complete mix, because that is likely to have an impact on the wanted speech -- although there are some very sophisticated digital noise reduction systems now that are pretty good with this kind of thing, like the CEDAR DNS boxes.
The other issue is that most of this is live, so the solutions need to be real time and easy to implement and adjust, rather than complex post-production systems.
Where it is possible to get at the pitch effects independently of the commentary, then it should be possible to process to reduce the horn noise. But if some broadcasters want to keep the authenticity and some don't, you're into providing two separate feeds and there may simply not be the cabability of doing that.
There is also the issue of getting the appropriate processing equipment out to South Africa with people who know how to use it. I know the Beeb ship out a lot of gear to handle this stuff, but I very much doubt they included a bunch of CEDAR boxes!
Here are some links to articles I published in Line Up magazine (the journal of the Institute of Broadcast Sound)over recent years which you may find illuminating and educational.
Technical Editor, Sound On Sound