Wizards can do anything, yes, but that anything often comes at a price. Often, that price is time they have to invest for things that a mortal could do in a matter of moments. Other times the price is higher.
Look at Fool Moon. Harry summons a demon AND trades part of his name to get something that Murphy could have gotten in 5 minutes on wikipedia with no cost at all.
Add to that the capability of specializing on something and a mortal can be crazy powerful. Not as powerful as a prepared wizard, but he doesn't need a millennium to adapt to a new situation. When you play up the downsides of magic, having a pure mortal around can be a real benefit. Keep in mind that one of the downsides of magic can also be that you are going to try to solve every problem with magic, when it isn't always necessary.
Look at the writeup of Marcone. He's got no powers but he's got tons of powerful stunts that let him do all kinds of things. He's out of his depth when it comes to purely supernatural encounters, but he's got a lot of ways to prepare for that kind of thing.
Not to mention that, as long as he isn't getting taken out, the pure mortal just keeps on going. The wizard is going to blow his last load sooner rather than later and while the pure mortal might be a bit winded by then, he'll just keep going.
Then there's the whole political angle, if you want to play that up. If a wizard does something, he always represents the white council, if he wants to or not. His actions will, in the worst case, fall back onto the council. That includes having the code of hospitality forced upon yourself or the unseelie accords invoked against you. That doesn't work on a pure mortal. You might not be protected under the accords yourself, but you don't have to oblige by them necessarily either. You break those rules at your own risk, but you are far more able to do this than any of the wizards.
Add to that: thresholds. If you have to act quickly inside of a threshold, the wizards will be fairly useless until they get invited. Or if there are circles in place to diminish their power.
All in all, there are lots of ways to engage a pure mortal and have him be useful.
When it comes to high powered games, pure mortals lose out a bit, as their +2 refresh bonus tends to pale in comparison. I think I remember there being a thread about this that proposed an adaptive bonus rather than a static one. I think we agreed on something like +1 refresh bonus for every 4 refresh for a pure mortal was the number that was suggested as a good solution. I'll see if I can dig up the old thread.
Then again, you could also go "pure mortal in name only" and take up some refinement for some enchanted items. You can easily justify this by the wizards you know, they are building the stuff, you are just paying for it with your refresh, since you're the one who uses it. We did a custom power like that as well, which basically gives you enchanted item slots to fill with various items per the enchanted items rules.