The analogy might not fully hold. The risk is that the controlled burn gets out of control. IIRC there was a case last year in Nevada where a controlled burn turned into an extremely large fire. A better analogy might be safety drills at Nuclear power plants. Done well, it helps ensure safety protocols are in place that can mitigate a big disaster, done badly, and you have Chernobyl.
> not letting the small fires eat away at a certain portion of the forest
Funny enough, small fires are very healthy for many forests and even _necessary_ for some. For example, Some trees do not drop seeds until there are fires. EG: "Giant sequoias are the largest trees on Earth. They can grow for more than 3,000 years. But without fire, they cannot reproduce." [1]
Further, the clearing of underbrush can be good for animals as they can move around more easily, hunt, gather, etc.. [2] Though, what is really not good for them are the mega-fires that burn so hot that it burns trees & everything 100% up to the top of the tree (killing it) and also several feet underground.
So, perhaps another analogy is that every year is like adding gunpowder into the forests. Setting this alight every now and then is good, but let it build up too long and it becomes a bomb. Areas that have burned in the PNW tend to look really healthy 1 to 3 years later. On the other hand, areas that have "over" burned in California with mega fires are drastically impacted, as if a nuclear bomb had went off and killed everything.
At the end of the day, prescribed burns is an amazing tool to create a defensive patch work of lower-combustion areas that help prevent fires from becoming mega-fires that are super-impactful to everyone and everything.
[1] https://www.pbs.org/wnet/nature/giant-sequoia-needs-fire-gro...
[2] https://www.pbs.org/newshour/science/explainer-how-wildfires...