I've used Kohler Command engines for years with great satisfaction. You're right about getting good service from Briggs engines if properly maintained, but until the last five years or so Briggs didn't really make a commercial grade engine with pressure lube and oil filtration. They did put oil pumps and filters on several engines, but the pump just recirculated the oil from the sump through the filter and back in to the sump.
I, too, have experienced some problems with the starters made by Denso who is probably the largest manufacturer of starters for the outdoor power equipment market - used by Kohler, Kawasaki and others. I usually just replace the solenoid and all is well.
The fuel pumps used by Kohler are made by Mikuni and also widely used by other engine manufacturers. The problem with them is usually dirt or varnish from old gas and/or neglected fuel filters.
The only problem I've had with the Kohler Command engines themselves is a blown head gasket at about 1000 hours on a 25 hp horizontal on my now 11 year old Grasshopper. Kohler did have some problems hydraulic lifters, bent push rods and with camshafts wearing one lobe flat. Ive seen other people with these problems. I attribute most of these problems to running the wrong oil or not changing it often enough. It is critical to run the recommended viscosity oil or the lifters will not function properly and ugly things happen to your push rods.
Jim