Anybody who gives a rat's ass about kosher, isn't going to be bringing non-kosher food in to begin with, and anybody who has non-kosher food, doesn't give a rats ass about your kosher-ness.
This seems like a troll, but I'll bite anyway. Kosher restaurants are often frequented by groups of people who include both kosher and non-kosher folks. For example, if your workplace has a going-away party for an Orthodox person, you will probably hold it at a kosher restaurant. This means that you get plenty of people in a kosher restaurant who don't care about kashrus.
Another problem is that different people can have different kashrus standards. If the restaurant is certified OU, then all food brought in needs to acceptable to the OU certifiers. If a person comes in who keeps kosher, but whose standard is one that isn't acceptable to the certifier, that won't work very well. Using the OU example above, OU would not recognize a Conersvative certification, but a Conservative customer would have no problem the other way. Similarly, the customer could have prepared the food themselves, and genuinely believed they did so correctly, but made a mistake. So the certifier can't rely on a customer's claims that outside food is kosher.