There are three things at work here.
First, the engine manufacturers oils have been notorious for having very large zinc contents,...keep that in mind. It's a very cheap and easy way to "skin the cat". I don't imagine engine manufacturers would get too much into oil blending. They kind of choose a catch all oil that will do and go with it. Why spend a lot of technical time testing all the different anti wear adds to pick the best, that's what the oil companies are for.
Second, there have been enormous amounts of data to prove beyond a shadow of a doubt that large doses of zinc are not really necessary. Especially if you look at the low rpm, low valve spring pressures, etc that small engines have. Many, many studies have shown that the zinc thing is somewhat overblown, with levels of 7-800ppm and above being plenty for most any engine.
Third, oil technology easily outpaces the manufacturers ability to test, approve and recommend oils on the market, not to mention they have no vested reason to approve someone elses oil.
So, let's put it all together. Unless you have some really special engine, which I'm totally unaware of, with special valve geometry and setup, then the oil technology has surpassed the "simple" solution of zinc being the one and only wear addative. Now, with that said, you can rely on almost any oil approved for gas (or diesel) to have something like titanium, boron, zinc or any combination of these to fully protect the small engine. The real worry for me would be the temperatures that air cooled engines work at. This is where a syn or HDEO would be my choice. Something like M1 would be a great choice. It's really hard for me to believe that an SL oil with loads of zinc would be better for almost any engine, than a modern oil with other wear additives in concert. The technology has surpassed the simple small engine.
I remember, back in the '70s and I was in high school mowing lawns for extra money, and I would be willing to bet me and certainly some of my pals used old briggs and tecumseh mowers that had the same oil in them for.......years at a time, that's right, years without a change. I remember tearing down my mower for 7th grade science class, and it was a clean as can be. I had put a quart of Gulf Multi G in it, who knows how long ago. From that day on and for many years clear up til I was driving a 1978 F100 V8 truck, I only used Multi G, simply because of that one sight of a clean lawn mower engine. I sometimes think today we fall into that same mindset here. We see one data point, good or bad, and it sticks with us as gospel when in reality. Back then, just as now, I could have probably put almost any decent oil in that lawn mower and they would have sold me a bunch of oil over those years.
Mower engines will run on water, for a lubricant, for years with no problem, they're tough. I worry more about hydro failures and using the correct fluid in them. I'm also not a fan of messing with oil additives. I let the oil companies do that. I doubt I can really improve on their engineering. We're not running high compression, high valve spring pressure engines in mowers, so we don't need to worry so much about protection like they do.