Even after six years of electrical engineering studies, and then another 20 years of design experience, it took a scary incident in my own home to give me a truly visceral feel for the danger of inadequate overcurrent protection.
Back in 2001, my wife and I hired a landscaping contractor to do some work at our place. Among other things, they installed low-voltage landscape lighting. There were four lighting zones, each with its own timer-equipped transformer box. Three of the four transformer boxes were mounted outdoors near the middle of their lighting zones, but placed in the woods surrounding our yard to be discreet. The contractor told me they needed just one 120V 20A circuit to supply all four 12V transformers. I added up the total lighting load to corroborate that, and then added the 20A branch circuit to my load center.
So far, so good. At least until we had some power outages. Every significant power outage required me to go outdoors, open up each individual transformer box, and reset the timer. A real PITA. Not to mention that the same drill was required several times each year as the daylight hours changed.

To solve that problem, I decided to bypass all the internal transformer-box timers, and control all four of the transformers from a single electromechanical timer switch, which I plugged into a 20A receptacle next to my load center. At time, I couldn't find a timer that was rated for 20A. But the total landscape lighting load was well under 15A, so I installed a generic 15A timer switch similar to the one below. Which worked just fine for the normal load, and now after a power outage I had only one timer to reset. It never even occurred to me that I should substitute a 15A breaker for the preexisting 20A breaker on that circuit.
Well, fast forward ten or fifteen years, and my wife had discovered that the outdoor receptacles that were installed for connecting the landscape lighting transformers were also really handy for powering strands of Christmas lights. And many years, she would install just a few more strands of incandescent lights. Until ...
Early one Christmas season, I was downstairs in my shop, and suddenly heard my wife yelling that smoke was coming from the closet where our load center lives. So I ran in to deal with it, opened the closet, and found that the 15A electromechanical timer was a smoking, blackened, melted plastic mess.

For a resistive load like a switch contact, the heat generated is proportional to the square of the electrical current. So at 20A, the heat generated is (20/15)^2 = 1.78 times greater than at 15A. Although the difference in current doesn't sound like a lot, the difference in heat generation is quite large.
Following that wake-up call, I well and truly bullet-proofed the landscape supply circuits. First I installed a second 20A branch circuit, giving one 20A circuit per pair of transformers. Then I installed a 30A power relay in series with each of those branch circuits, with both relays mounted in a metal junction box. Finally, I bought and installed another generic 15A timer, but now it only switches the coil current to those two power relays.
Nowadays, I'm pretty diligent about proper overcurrent protection.
Back to the original topic, Emerson requiring Shopsmith to specify 15A breakers makes a ton of sense. There's no other overload protection for the motor. Without at least specifying reasonable overload protection, Emerson would not only be exposed to warranty expenses for cooked motors, but potentially also to liability claims in the event of fire. The good news is that, unlike my landscape lighting timer, a Mark V is almost never operated unattended.