Using JOSM with the search filters:
"type:way highway:"    to select and count all roads
"type:way highway: (name: | ref:)"    to select and count all roads
that have names or refs
and roughly assuming real-world road = OSM way
I get the following statistics:

Johannesburg, from http://metro.teczno.com/
51866 roads
20842 roads with names
40.18% of roads are named

The provinces below are from
http://downloads.cloudmade.com/africa/southern_africa/south_africa/gauteng#downloads_breadcrumbs
and co.

Gauteng
62105 roads
27222 roads with names
43.83% of roads are named

Eastern Cape
21794 roads
9455 roads with names
43.38% of roads are named

KZN
46943 roads
37193 roads with names
79.23% of roads are named

Limpopo
4215 roads
1407 roads with names
33.38% of roads are named

Mpumalanga
22075 roads
9060 roads with names
41.04% of roads are named

Northern Cape
9261 roads
2500 roads with names
26.99% of roads are named

Free State
14191 roads
5486 roads with names
38.65% of roads are named

Prince Edward Islands
no roads are listed

North West
35554 roads
14886 roads with names
41.87% of roads are named

Western Cape
60505 roads
39916 roads with names
65.97% of roads are named

Obviously this isn't fully correct since roads running between
provinces will be counted twice, but:
Total roads for SA: 276643
Total named roads for SA: 147125 (53.18%)

Some further questions to ponder:
How did KZN get so many roads named?
Why is Joburg's road naming below the Gauteng average?
Does Limpopo really have only 4215 roads?
Is there really no roads on the Prince Edward Islands or are they not captured?

In Joburg, so few streets are named that most people and places I
visit weren't on it until I added them. What can we do to improve this
sad situation?

The relative road to province percentage conversion for Gauteng is as follows:
1 road = 0.00161017%
10 roads = 0.0161017%
100 roads = 0.161017%
1000 roads = 1.61017%
621.05 roads = 1%

Should we summarize this on the OSM Wiki page for South Africa?

Thank you
Damjan

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