Why is it impossible to realize elliptic even-order filters with \$R_S = R_L \$?
The elliptic filter response is equi-ripple in the passband. The gain ripples between unity and 'design dB down', where the filter is designed for 0.1dB, or 1dB, or whatever ripple.

An odd order filter has unity gain at DC, and design dB down at the corner frequency.

An even order filter is still design dB down at the corner frequency, which means it must also be design dB down at DC, as the order of the filter defines the number of passband ripples.

For a lossless filter, if the source and load impedance were the same, there could not be a finite loss at DC. To create the DC loss, the source and load must be different impedances. The action of the filter 'tunes out' the difference in termination impedances at other frequencies to achieve the unity gain parts of the frequency response.