I'm sure that my timing belt has been wetted with oil. It slings off. My timing belts always look fine when they come out.

My limited experience is that pushrod engines used cam chains or direct gear drive. When cams moved up above the valves, however, the distance between the cam and crank increased significantly, and manufacturers switched to belts, which are lighter, quieter, cheaper, and easier to keep tensioned.

A cam chain's load is pretty jerky. It is hard to keep a long chain gliding smoothly under those conditions.

In my mechanic days 25 years ago, Porsche used chains with the overhead cams on their opposed six cyl in the 911. The elaborate hydraulic tensioners and expensive chains that were required were one of the key routine maintenance items on those engines.