One legit reason would be if you have more than 8 inputs you need to record simultaneously but your interface only has 8 channels going to your computer. Examples could include when one sends all their drums to the mixer, or all the leads and backup vocals, or the horn section, etc. to the mixer to create a stereo or 4-channel sub-mix on the fly to sen to the interface, leaving 6-8 channels on the interface open for everything else.
Frankly, on the lesser-expensive mixers that you're asking about the preamps and EQs are usually not much to bother writing home about. Once you get up well into 4-digit retail prices and higher, the story can be quite different, of course. Those are the pres and EQs that have a character many software plugs try to (and usually don't entirely succeed) to emulate.
But even in the mid-sized mixers you can (if you don't go too small) find enough input/output paths in the mixers in the form of Aux buses channel inserts and such that allow you a very nice flexibility in where and how you can add high-quality outboard hardware in the form of compressors, EQs or reverbs to you recording or mixing chain.
Why hardware and not software? Because no two hardware or software devices sound the same; no two compressors, EQs or reverbs are created equal, and many analog hardware boxes have a character or sound that just cannot be duplicated that well by software.
G.
