The risk is not teeny tiny. The risk is fucking HUGE.
The probability is tiny - very few batches of formula powder are contaminated and pass through quality control. The consequences are very serious. Risk is calculated by probability x severity of consequence.
Yes, salmonella (when identified) can be treated quickly. When it isn't it can lead to gastrointestinal damage or death. When treated the prognosis is good.
Other bacteria - such as E. Sakazakii - don't have such good recovery rates even when treated. The risk of death is much higher and resulting complications include meningitis, brain damage, problems with the digestive system, autoimmune problems, respiratory problems, sepsis....
nannyl you sort of know me and I assure you I've known a baby get very sick with an E. Sakazakii infection, which has left her with long term health problems :( There's pretty much no other way she could have got sick and I don't think her parents will ever forgive themselves knowing that it was very probably preventable.
You can still make bottles up (using 70C water) and cool them and store them in the fridge, which is immeasurably safer than using cooled, boiled water. Once you've reduced the level of the bacteria in the milk, by using hot water, and cooled it to below a temperature where bacteria can thrive, the milk will remain not sterile but safe.
Bacteria cannot grow in the powder, but they can be introduced at any stage of the preparation process and once the powder is opened and exposed to moisture then bacteria can start to grow again, which is why most tins of formula will say 'use within 3 weeks' or similar.
As you say, not doing it doesn't guarantee illness, but doing it properly pretty much eliminates the risk.