There are a number of reasons a studio might incorporate an analog mixer as well as the DAW interface [flexibility in routing signals while recording, etc], but most commonly it's to take advantage of the analog sound quality the board would offer. Many mixers like to mix in the analog domain, for a variety of reasons, including the experience of working with the physical controls, but analog mixing is often done to benefit from the sound of the analog circuitry -- transformers, transistors, etc, all contribute a little analog warmth & grit, and summing [mixing] the tracks trough analog summing amps is a popular approach for those who feel that there's nothing like the real thing to get that warm, rich analog character.
A traditional analog mixer would not be a control surface for the virtual DAW mixer -- those can be found at various price points, and don't require any analog signal path. Analog mixers -- especially high-end mixers -- are primarily desirable for the sound quality they bring to the party.
That said, with the convenience of mixing in the box [with the DAW's virtual mixer] it's not uncommon for a mixer to combine virtual mixing with analog mixing -- some people refer to this as hybrid mixing. The mixer will utilize an analog signal path when he wants the contribution of real analog circuits, while taking advantage of the power of plug-ins and virtual mixing advantages for other tracks. Everyone has their own preferences, and it's pretty common to see digital & analog mixing environments combined..