Q.Why do we consider frequencies above 70.7% of the maximum gain for bandwidth?

Bandwidth is defined between the standard half-power points of the response curve. …

[!TLDR]

The 70.7% (0.707) gain points are the half-power (−3 dB) points that define bandwidth.

Power is proportional to the square of the gain (voltage). When the gain drops to $0.707$ of its maximum, the output power becomes $(0.707)^2 = 0.5$, i.e. half of the maximum (mid-band) power. These are called the half-power points or −3 dB points, and the range of frequencies between the lower point $f_L$ and the upper point $f_H$ is taken as the bandwidth ($BW = f_H - f_L$). Below and above these points the amplifier is considered to give too little output to be useful. …