I don't know that it really matters how gross any adults/other customers may be; allowing little kids on the counters is a bad idea, not only because they frequently grab things (often sticking them in their mouth in a fraction of a second) and sometimes diapers leak (what parent among us *hasn't* experienced a poosplosion? Seriously, I'd like to shake your hand and learn your secrets ), but because there's also huge liability concern associated with an unsecured child potentially falling (or jumping) off the counter and getting injured. There's simply not a good reason to allow it.
Regardless of what policies are made re: counter sitting, it would be a good idea to keep some lysol wipes on hand for a quick counter cleaning after particularly grody customers of any age.
I've known many people who lick their fingers to leaf through papers. You don't know who's done that or who hasn't before they came in to the store. I see that as no better or worse than a child putting something into their mouth. Some people also have various other disgusting habits that I don't want to come in contact with, which is no worse or better than a small child's propensity towards snot and drool. It happens.
My niece is past putting things in her mouth. When she's sitting/being held close to an adult's body, she knows that she has to keep her hands to herself. If she's on the floor, she's running. I'm more worried about her running around and hurting herself, damaging floor displays, or something worse happening to her if she gets to the door. I'd much rather have her right next to me than having to chase after her while I'm supposed to be completing a transaction. Whenever I have her on the counter, her bottom is on it and I have an arm around her and am standing right in front of her. She would actively have to work quite hard to end up falling, and even then, I'm still close enough with an arm around her that I could catch her.
I'm not saying that I'd disrespect any company that had signs up. But if they don't have any signs, I'm going to hoist Sproglet to the counter. In my situation with my niece, that's the best option for me. It won't be the best option for everyone, but I highly doubt that her back end or hands are inherently more gross than many of the adults that come in simply because she's a child and it's her bottom.