ALL filters regardless of type, shape or order are defined by the half-power points in the passband or -3.01 dB or 0.707 V. This is simply the amplitude response by definition defined by half-power.
But, there are many other complex filters that have more important specs like linear-phase or group-delay flatness to -6 or -12 dB or PB ripple in dB using higher Q offset f for steep skirts or band stop BW and attenuation. For Chebychev Filters the skirts are steeper by staggering higher Q filters and the equal ripple filter is defined by the BW limited by the ripple in the band and where it exceeds this dB ripple at the edge, which is more important than the half-power point. (ty LVW)
This is why no other value is used for basic passband amplitude response.