I have to disagree. Rotary encoders and faders are
the way to make smooth, gradual changes to various parameters by gut feel, which is more or less what a mixer is actually doing.
When money is no object, music is both mixed live and produced in the studio on enormous digital consoles which replicate their DSP parameters onto hundreds or thousands of tactile faders and rotary encoders.
The keyboard and mouse are a terrible way to mix. Fortunately small physical control surfaces can be had for not too much, though then you have the problem of matching your limited controls to the thousands of parameters in the DAW.