I am under the impression the issue with engine braking is the extra stress on the valves, not so much the clutch.
I think I remember someone saying the exact same thing about incandescent bulbs
that just seems that way, because of … you know … survivor bias
. . . and use a toothbrush with firm bristles to do the best job of scraping plaque off.
It’s been decades since I’ve even seen a toothbrush with anything but soft bristles.
Also, do people still put raw steak on a black eye?
This. Even in an automatic trans, downshift for long descents, and don’t ride the brakes. The routine ups and downs of rolling terrain? Don’t bother.

I am under the impression the issue with engine braking is the extra stress on the valves, not so much the clutch.
Which valves would these be? And why?

Things checked in a tune-up:
You forgot changing the rotor and distributor cap. Be sure you time your engine afterwards.
The cylinder exhaust valves. I am sorry if that was not clear. Im sure there are quite a few ‘valves’ in the various systems on a modern engine, but the cylinder valves are a primary component of a gasoline engine.
My understanding is that engine braking puts stress on the valves. This makes sense to me. The transmission and clutch are part of the drive train and obviously involved too, but ultimately its cylinder compression doing the work.
I believe I first heard it on the old CarTalk radio program, with the speaker stating that brake pads are cheap and cylinder heads are very expensive, probably a very long time ago. A quick google search returns several results saying it should not be a concern.
No, that doesn’t make any sense. The valves are closed during compression, so the material doesn’t experience any strain. Now, the lifters and springs might get a tiny amount of exercise, but so what- they last for billions of cycles.
The clutch will definitely get some extra wear each time a downshift happens, but that’s probably negligible.
In engine braking, where is the heat deposited? It’s got to be somewhere.
(note: This is not meant as a snarky gotcha question. I don’t know the answer, either. But heat has to be deposited somewhere, and wherever that is, I would expect that there would also be wear).
Thought question:
What generates more heat? The combustion of air+fuel in a compressed cylinder, or just the compression of air alone in the same cylinder?

To his dying day, my father recommended the practice of routinely slowing a car by downshifting, so as to save wear and tear on the brakes.
Maybe not routinely but I drive a manual in Minnesota winters and sometimes downshifting is safer than braking on slippery roads. Dumping momentum into your power train can slow you when there just isn’t enough friction with the road to do the job; the automobile equivalent of air brakes.
Pennsylvania used to have some absolutely brutal winters. During those times I would shift into a lower gear when descending some of the icy hills in the area. It definitely helps.
It’s been quite awhile since we’ve had a really bad winter.

One I have heard is that is no longer necessary to do a “software shutdown” before shutting off a computer with the power button like you used to have to do in the 90s/early 2000s. The power button is now triggering the minimal software shutdown, rather than just cutting the power.
My computer doesn’t even have an “off” button; the Power button is strictly for turning the computer on, and pushing it when it’s already on just does a reboot. Turning the computer off is done entirely through Windows Start menu’s Power options (though on rare occasions I’ve been locked up badly enough to have to yank the power cord).

But I don’t always bother to turn off the switch when unplugging something (it isn’t unsafe to do this), and I do encounter people worrying about that, on some sort of safety grounds
Hmm. Here on the west side of the pond we have no wall switches. Everything unplugs. About a billion times a month.

My understanding is that engine braking puts stress on the valves. This makes sense to me.
Can’t have too much of a deleterious effect, otherwise the log trucks and other diesels in my neck of the woods wouldn’t use compression brakes. And prefereably not at 4 a.m.!
My 6 speed Allison transmission allows me to shift into a manual mode, and pick a gear. Has been most helpful coming down from Government Camp, 6% grade, while carrying a camper and towing a 7500# boat. Keeps me from having to ride the brakes, and haven’t seen any problems
in 80,000 miles.

I remember carbohydrates being recommended as the core of a healthy diet - literally, ‘people should eat more pasta’.
Especially obnoxious were the more militant “Save The Earth” types who condemned eating meat as a decadent luxury, when we could feed so many more hungry people on this overcrowded planet if we all lived on beans and rice. In my more trollish moments I’d declare that I would kill and eat their children before giving up meat.
I forgot about the wall switches. Discovered those years ago while visiting London.

I also have this nagging suspicion that there will suddenly arise some obvious and serious reason why ‘being in ketosis’ was a terrible thing to seek to achieve.
Oh quite possibly. However in my case I think it’s less dangerous than being 110 lbs overweight.

It’s been decades since I’ve even seen a toothbrush with anything but soft bristles.
Every style of toothbrush comes in soft, medium and firm. I’m a medium guy.

No, that doesn’t make any sense. The valves are closed during compression, so the material doesn’t experience any strain. Now, the lifters and springs might get a tiny amount of exercise, but so what- they last for billions of cycles.
The clutch will definitely get some extra wear each time a downshift happens, but that’s probably negligible
Yeah, if valves experience significant additional wear under deceleration, then semis with Jake Brakes would just be eating valves on the regular, and they’re just not.

In engine braking, where is the heat deposited? It’s got to be somewhere.
The heat generated (other than a minimal amount in the clutch surfaces) is in the work done to compress the air in the cylinder. So that heat is removed through the cooling circuit and out the exhaust.

Thought question:
What generates more heat? The combustion of air+fuel in a compressed cylinder, or just the compression of air alone in the same cylinder?
It’s got to be the air+fuel compression. Leaving aside the complication of variable valve lift and timing, the compression ratio (and associated heating) will be the same, so I don’t see how adding fire could be anything less than more heat.