Unfortunately this doesn’t seem to cover the explanation for the process, but I did find an explanation (linked in my other comment)

I tried many years ago but couldn’t readily find an explanation for the process/reasoning, but I did find one now in the video here and it does make sense I also checked Wikipedia and learned more:

All fluoridation methods, including water fluoridation, create low levels of fluoride ions in saliva and plaque fluid, thus exerting a topical or surface effect. A person living in an area with fluoridated water may experience rises of fluoride concentration in saliva to about 0.04 mg/L several times during a day.[3] Technically, this fluoride does not prevent cavities but rather controls the rate at which they develop.

Fluoride’s effects depend on the total daily intake of fluoride from all sources.[51] About 70–90% of ingested fluoride is absorbed into the blood, where it distributes throughout the body. In infants 80–90% of absorbed fluoride is retained, with the rest excreted, mostly via urine; in adults about 60% is retained. About 99% of retained fluoride is stored in bone, teeth, and other calcium-rich areas, where excess quantities can cause fluorosis.[79] Drinking water is typically the largest source of fluoride.

Wouldn’t it be better to give families vouchers for toothpaste and toothbrushes? Or have subsidized lower price ones available?

I never really understood how water briefly swishing through your teeth with some minimal amount of fluoride in it has any effect on the teeth. (edit: explanation in the replies). Fluoridation comes across as a way for industry to legitimize toxic waste instead of having to treat it and dispose of it responsively and ecologically.

Meanwhile we are ingesting it when drinking tap water, along with our pets and all other animals that have access to the water supply, and we wash our hands with it and shower with it, and we ingest it further through crops/food that is grown/prepared with the water.