I was wondering why is the ideal AF has zero value in all the function except in (0, 0).
An ideal ambiguity function is by definition a Dirac Delta function with an impulse response at 0 delay and 0 frequency with zero value elsewhere. It only takes on a non-zero value when the delay and frequency are matched between the filter and the signal.
That is of course not the whole story as that doesn't address why this is a useful definition. This definition is chosen so that there is no ambiguity as to whether the signal and filter are matched. If they are not matched then the response is zero.
As the Wikipedia link above states, this is not usually desired in practice as there will usually be some mismatch between the filter and signal:
This is not usually desirable (if a target has any Doppler shift from an unknown velocity it will disappear from the radar picture)...
In practice one often wants an ambiguity function that is close to the idea, but not exactly to handle mismatches in the delay or frequency offset.