I think the confusion is due to you thinking of the total number of cell divisions, while I am thinking of the number of divisions separating a given cell from the zygote.
This lead me to misunderstand the relationship you were claiming between "This is not how the body operates" and "skin and gut cells reproduce far more often than normal".
Bone marrow for example needs to continuously create Blood cells with a short lifespan. (Adult humans have roughly 20–30 × 1012 (20–30 trillion) red blood cells at any given time, comprising approximately 70% of the total human body cell number.) https://en.m.wikipedia.org/wiki/Red_blood_cell
Thus your bone marrow must create new cells at a much faster rate than average, making the average a meaningless number.
Now you might think you could design bone marrow to minimize the number of generations nessisary to produce that blood, but it does not operate with such efficiency. In large part because fewer cell generations does not mean fewer mutations.
If you check the paper, you will see it describes a scheme that minimizes the number of generations while maintaining the observed rate of cell division. The average rate of division across tissues isn't really at issue here, tissues that require fewer cells will just have a shallow hierarchy.
>"it does not operate with such efficiency"
Most likely it does not operate at max efficiency. However, since most mutations seem to occur during mitosis, it would make a lot of sense for natural selection to optimize (number of divisions)/(generations from zygote).
First, it's not the number of generations that are the direct risk. A cell that does nothing will still mutate over time. It's large numbers cells that share a few risky mutations that are the problem.
If you have a 1,000 cells that can do 30 generations without hitting programmed cell death then a single mutation that kicks that off can form a large mass without tripping your body's alarms which also share that mutation. Even if they end up as a non cancerous mass that large mass is very likely to cause problems.
On the other hand if you have 1 billion cells that can each do 10 generations and they all formed young you still get the same 1 trillion cell potential, but don't risk that single mutation as those 1 Billion cells showed up at a young age. Further, when some of those 1 million cells start growing uncontrollably they only grow to 1,000 cells before hitting programmed cell death which is a lower cancer risk.
Now sure, the body can play around with these numbers to form a crazy number of skin, gut, and blood cells from some relatively small cell pools. But, it's already playing those games while minimizing cancer risk. So, we don't have some pool of 'young' cells to solve problems late in life because it's to dangerous to keep them around.
PS: People often thing of their body's as kind of a tub of undifferentiated mass. But, cells a body structures are optimized for a huge number of problems that only become obvious with deep investigation.
>"First, it's not the number of generations that are the direct risk. A cell that does nothing will still mutate over time. It's large numbers cells that share a few risky mutations that are the problem."
If this is correct, I think you would likely be right. Do you have a reference?
This lead me to misunderstand the relationship you were claiming between "This is not how the body operates" and "skin and gut cells reproduce far more often than normal".