A lot of people complained about the Tecumseh engines being junk. Back when Tecumseh was still in business early 2000, Briggs had like 66% of the market, and Tecumseh had like 13%, and my Briggs to Tecumseh failure rate was 15:1 So they were not that bad of an engine from my own experience.
I am a fan of the old cast iron tecumseh engines. I still have and use a HH120 and a VH100. Got a few others laying around. Just not a fan of the newer push mower engines. Lots of broken con rods on the MH engines too.
And after that series with the connecting rod issues, Tecumseh beefed up their connecting rods, and very seldom did one break after that unless ran without oil. The internal components on their V twins were overbuilt and had massive connecting rods and bearing surfaces.
For some dumb reason they do. Some think the engine is too loud so they run it about about half throttle. I remind them that they are dealing with an "Air Cooled Engine" and when they run the engine slower they are also slowing down their cooling fan. I ask them if they would run their car's radiator half full?
It was somewhat of a rhetorical question and I know people do idle them down for the reasons you mentioned but is it really necessary? It's all personal preference of course but if I'm only taking 10 or 20 seconds to move something I just let it run full and keep as much cooling air flowing over that engine as possible.
Was the mower deck orange and the engine gray? We had one when I was a kid. It worked fine but was hard to restart hot.
The bad thing about Tecumseh engines was what I heard my former boss and mentor say many times. "You have to be a mechanic to work on a Tecumseh not just a parts changer."