This is a difficult subject to discuss because there are so many variables. Synthetic oils often do not have much, if any, zddp content, but some do. I suspect the manufacturer will tell you that if it does not, it has other wear additives which are sufficient. Whether or not they do the same job is open to debate because there are so many variables in the discussion.
Obviously, so they tell me, is the type of camshaft being used. If one has a roller cam, then there is little to discuss. Quality oil of most any brand should be sufficient. If one has a flat tappet cam, then it makes a big difference if one is running an 80 lb valve spring or a 125 lb valve spring. Then, we have the question of #3 Exhaust cam lobe which is not positioned correctly in our Buick engines so the lifter does not rotate as fast as the other lifters.
I suspect there are a lot of engines out there that have seen all kinds of oils and survived.
Personally, in my T with a factory cam, I have run Valvoline Racing 10-30 for many years.
Now, there are a number of others that run similar or higher amounts of ZDDP. Lucas, Shaeffer, Brad Penn, Joe Gibbs, Amsoil, and others make higher ZDDP oils for use in older flat tappet engines. Some may be synthetic. Some Mobil 1 Racing oils have a lot. Mobil 1 20-50 used to have more than their 10-30s and other lighter weights. I have not checked lately.
There are a lot of people that use Shell Rotella diesel oils under the belief that it has a lot of zddp in it. Research will show that most of their oils cut back on the zddp years ago. I am not sure if there is any that still have a goodly quantity in it or not. Believing what people post on the net is a quick way for entry to hell, I suspect.
There are many zddp additives out there. Some shysters have made a good living out of selling them. I believe that the oil companies are right in that adding such to carefully blended oils is a good way to screw up good oil and I don't use them.
