DAVE C. - Non detergent oil is only recommeneded by Kohler for the initial run-in of rebuilt engines, first 5-10 hours of running. And frankly, I don't even like to use it then, typically I use whatever oil I plan on running for break-in, like my 15W-40 or 5W-40 Rotella.
The old IH FARMALL engines had "State of the Art" oil & air filters for their time, but unfortunately the state of the art wasn't so great back then. Yes, the non-detergent oils did not dissolve deposits, they actually helped deposits accumulate, the filters just removed the BIG chunks when they broke away from whatever they were clinging to, and eventually sludge formed which impeded oil flow and return to the pan. Kohler's have good air filters, at least after the 70/100's came out, the dry pleated paper filter elements do a great job, but no oil filters, so oil changes are used to remove deposits and accumulated dirt/deposits in the oil.
A good detergent oil like Rotella, or Mobil Delvac will eventually dissolve and remove those deposits and keep them from re-forming. When you open the engine up for rebuild the inside of the engine will be clean, oil can get to where it's needed and then return easily to the oil pan. I had the valve covers off my Powerstroke diesel engine in my pickup around 250,000 miles to replace the glow plugs and the tops of the heads, great place for sludge to start forming was spotlessly clean. The '51 Farmall M was pretty well sludged up when I got it 8 yrs ago, two changes of Rotella cleaned it up inside too. When SON & I reset the valve tappets 5-6 yrs ago under the valve cover there was no sludge present.
Not sure about the Mobil Delvac oil, but I know Rotella has enough ZDDP additive, and I suspect the Delvac has it too, to prevent accelerated cam lobe & lifter wear that today's gasoline rated oils do not have. No need to run an expensive oil suppliment.
The private branded oils sold by Kohler and B&S would also have enough ZDDP, but probably not as strong of a detergent package in them.
29 yrs ago when I rebuilt my K241 the first time, I broke it in on 10W-40 Valvoline, then about a year later switched to 10W-40 Arco Graphite oil, it had powdered graphite blended into it as a dry film lubricant additive, that oil was coal black right out of the can, but I guess nobody else used it, it went out of production after only a couple years. Then I used Valvoline Turbo V 10W-40, had a better high temp additive package to resist high oil temps in turbo-charged gas engines which were becoming popular. Air-cooled engines run hotter than water-cooled engines so I used it for several years. Then in 1996 when I got my PSD I switched everything over to Rotella 15W-40. The graphite powder in the Arco oil left a thin black deposit in the engine the Turbo V didn't remove. But 8-9 yrs of running Rotella cleaned it right up. When I pulled the engine apart back in 2006 after 20+ yrs and 1400 hours of running it was squeeky clean.
Dad had a small fleet of CC's years ago, 7 or 8 IIRC. Couple of them used oil. He used to buy whatever automotive oil that was on sale, then switched to IH #1 Low Ash 30 weight oil in them. He ran his CC's ONLY in summer. The Kohler's that burned a little oil stopped burning oil, smoking on start-up stopped. Sticking exh valves freed up. So it's not a bad choice for CC's run in summer only.
Probably the most important thing about engine oil is to change it when recommended. Either keep track of hours run with the hour meter on the tractor, or the way I like better, is to keep track of gallons of gas used. Change the oil after every 30-40 gallons of gas used. That takes into account the hard pulling high gas consumption running with higher engine temps, and the light load putt-putting around the yard we all do from time-to-time with low gas usage and relatively cooler engine temps that isn't as hard on the oil.