Why is the gain of the amplifier not considered in the frequencycalculations?
In simplest terms, it's because they are looking for a relative value when they write "3-dB-frequency" (which means \$-3\:\text{dB}\$.)
Say \$V_o=\kappa\cdot V_s\$ (with \$\kappa\propto \mu\$.)
\$V_o\$ depends on both \$V_i\$ and \$\kappa\$.
\$V_i\$ doesn't depend on \$\kappa\$.
Since \$V_o\propto V_i\$ when \$V_i\$ is \$-3\:\text{dB}\$ down, then \$V_o\$ will also be \$-3\:\text{dB}\$ down.
The \$-3\:\text{dB}\$ point doesn't depend on \$\kappa\$.