Pushrods and rocker arms universally used on classic British twins. The objections are noise, frequent need for valve clearance adjustment, and limited rpm ceiling as a result of extra valve-train weight; for equal rev capability, a pushrod valve train requires roughly twice as much valve-spring pressure as does an overhead cam system.
The usual Japanese solution has been chain-driven double-overhead camshafts—one cam for the intake valves, another for the exhausts—with some form of automatic chain-tension adjuster. As chains wear, accurate valve timing is lost, which is why Superbike teams of the 1990s were supplied with gear-drive kits. I love that gear-drive sound!
DOHC driven by spur gears is the racing solution because, with either finger followers or inverted-bucket tappets, it gives minimum valve-train weight and therefore maximum valve control. But spur gears are expensive and noisy, so they aren't used for production designs. EPA sound meters are listening!
Toothed rubber belt and cog pulleys. This was how Ducati eliminated the handwork once required to assemble Dr. Taglioni's shaft-and-bevel cam drive (selective-fit shims, checking tooth-contact patterns with Prussian blue, many trial assemblies, hours of work). Belts were great at first, even Rob "Mr. Superbike" Muzzy was interested in them in the early 1990s. But as valves had to be accelerated harder and harder in Ducati's Superbike program, belt life became so short that Ducati gave its ultimate V-twin, the 1199 Panigale, cam drives of steel chain.
Weird and wonderful. Husqvarna's engineer Folke Mannerstedt developed his Excam system in 1927. Its cam oscillated back and forth rather than rotated, so it could be driven by a connecting rod from a half-speed shaft geared to the crank.
Shaft and bevels—what Kawasaki chose for the W800—is a system that was widely used in aircraft engines of both world wars and which stuck in the minds of those exposed to it. As a result, Norton's Manx racing single and Velocette's KTT employed it. Why Kawasaki, why now? Maybe for two reasons: First, it's different, and identity is priceless today. Second, with its splined vertical driving shaft, there is no change in valve timing as the engine expands during warm-up and no noise. How did they get around "the Taglioni problem"? Uncounted millions of cars and trucks drive their wheels through shaft and bevels, all so accurately manufactured that no hand-fitting by elderly craftsmen in wire-framed spectacles is required.