Bandwidth of a system
It seems that you are speaking about the bandwidth of a lowpass system, right?

At first, you should realize that the bandwidth of a system is a parameter that needs DEFINITION. Hence, in some cases, you can define the bandwidth for your own purposes even at 1dB or 2dB points. But that it is not the core element of your question.

(1) Your graph shows a lowpass response according to a so called "Chebyshev behaviuor" (with gain peaking higher than the value at f=0). Indeed, for such a transfer function it makes sense to specify the bandwidth at that frequency where the magnitude crosses again the DC value (horizontal line). 

(2) However, if the magnitude response does NOT exhibit such a peaking (lowpass response according to a "Butterworth" or "Bessel") it is commonly agreed to use the classical 3dB frequency (3 dB below the DC value).   

Summary: The bandwidth of a lowpass system is a matter of definition. In general, it defines the end of the "passband" based on an acceptable "ripple" (magnitude variations) within this frequency band. If, for example, the gain peaking (in your figure) is w=1 dB it makes sense to specify that the ripple within the passband is 1 dB only. For another system without such peaking (typical example: Butterworth response) the magnitude variation (ripple) would be 3 dB. 

Remarks: As you have made reference to a wikipedia contribution: Please note that the mentioning of "3 dB below peak" applies to a bandpass system only. And even this is a matter of definition - for some bandpass systerms it makes sense to require 1dB or 2dB break points. For lowpass responses the explanations/definitions apply as outlined above.

Please note that most filter design aids (tables, programs) are using bandwidth definitions in accordance with the above mentioned two cases.