Here is a link to a Penrite Technical Bulletin on Zinc in engine oils, including a bit of history. It also points out that the present 800 ppm P limit, only applies to ILSAC grades, and not to xW-40 or heavier oils
http://www.penriteoil.com.au/tech_pdfs/0Zinc Myths & Legends Nov 2014.pdf
Also here is a VOA from Castrol Edge 10W60 from a few years a go
Here is a VOA from a few year a go.
http://www.bobistheoilguy.com/forums/ubbthreads.php?ubb=showflat&Number=2988455
aluminum 8
iron 1
silicon 7
titanium 47
moly 198
boron 59
calcium 2823
phosphorous 804
zinc 922
You can see the Phosphorus is at the 800ppm limit (with Zinc at a little over 900ppm), but it also has a decent amount of Moly, Boron and Titanium. All these do similar jobs, without being included in the P limit (i.e. ZDDP or ZDTP).
This is a modern 10W60 oil, so it has no P limit, yet they have still kept it to the 800 ppm P limit anyway.
The API SF and SG oil P limit is 1000ppm, yet many were around 800ppm anyway (according to Penrite). So just because it's SG, it doesn't mean it is high P (and therefore Zn), it just means it could be. It depends on the actual oil.
The take home I'm getting from reading around, is that they don't need as much P anyway, as they have improved the chemistry over time.
If you want a high Zinc oil, go for a HDEO or a street suitable racing oil (like VR-1) or a HM oil. But also consider the top shelf synthetics like M1 or Castrol Edge 0W40, maybe not as high in Zinc, but wear is well under control.