The FDA does not prescribe that three batches must be used, but three is the minimum number of batches that needs to be used to generate adequate and relatively facile statistical support. Two- batches statistics would be much more difficult to generate. Of course, any company can use more than three validation batches if it so desires. However, companies typically select the minimum - 3 batches - because it is the cheapest and yet acceptable option.

You can defenetly try to use less than 3 runs to go for approval but you would rather try to minimize the risk of failure by doing three instead of trying to convince any auditors to have enough information with only one run.

3 is a gold number since more thand 40 years in the validation activities. Initially when I began working in the pharmaceutical industry my boss told me : Once is a luck, twice is a special circumpstancy and three is a validation.
Nowadays, 3 is not anymore a gold number if you can justify to use another number by performin a full FMEA study on the cleaning process. Sometime it can be even more trial if you consider such activity shall be supported for validation on another type of consecutive activities.

Three is just enough to have an average, higher limit and lower limit. Nobody wants to do more than absolutely needed. The number however, also depends on (future) risk assessments and process optimizations: how critical are the highest levels detected to influence the next processing step(s) and product quality. If the impurity is of high risk, a more reliable statistical number is needed. Normally three is the golden standard as Franck wrote, and observing the analytics of subsequent cleanings will give more reliable statistics that might be presented later on.

It is not impossible to use only one batch but you have to be very very strong to proove to the FDA that one is sufficient with a lot of reliable documentation. I personaly never seen that but an FDA inspector told me that it happens...

This is just a hearsay. I do not believe it. We cannot conduct discussions on this basis. Statements need to be supported by evidence. In this particular instance it would be impossible to determine margin of errors, standard deviations, etc. Any future process would need to reproduce exactly the validation run! In real life this is impracticle...

We are all saying the same, 2 is not enough and 3 might fit the requirements so you can try less but we recommend at least 3.

This is for statistical reason. One can use two data points also, but variance will be very high and degree of freedom will be one. Minimum data required for Gaussian distribution analysis is three (because two data points are always linear) with degree of freedom two, if we assume there is minimum errors in the measurement. Therefore, in any measurement, three minimum pints are required. But more number of experiments provide more confidence lower variance.