This was a new one for me. I got a request from a potential new customer to come visit their dog each night that they stay with me. Have you done this before? Obviously I feel like saying "yes of course," but I do wonder if this would actually be MORE stressful on the dog to see their owners come and go. I'm curious any thoughts other sitters have.
The closest thing I've encountered was for a couple stays over ten days, the owner requested if her adult daughter could stop by. I suggested it would be better for us to visit her at her home which was nearby. It was a really nice time for all and went great. Daily visits seems a bit excessive. Perhaps you want to explain you don't have an issue with it, but are concerned if the coming&going may be stressful for the dogs and you'd like to take it 1 visit a a time and see how it goes.
I'd definitely be concerned that it would be more stressful for the dog (and you). Like Deb said, I'd suggest less frequent visits and meeting somewhere away from your home. Of all the dogs I've watched, there have been maybe one or two who didn't sulk for a while when their owner dropped them off, no matter how many times they've been here. However, the dogs that I've gone to pick up from their home have been happier to come with me (We're going on an adventure! Whee!) and adjusted much more quickly to my house because they didn't get 'abandoned' here.
I often watch dogs who are in town visiting with their family. On a couple of occasions I have had requests for owners to stop by and take their own pup for a walk (recently one even offered to take my dog with them ;) ). This is perfectly reasonable to me, but they have never asked to visit their dog EVERY night. Usually once or twice a stay, depending upon the length of the stay. I would say this is entirely up to you. I have some regular guests who are very "stranger danger" and people coming into the house put them on edge, so meeting your guest outside would make it easier. It's hard to decline that sort of request, but as long as you explain that it is in the best interest of your household folks should understand.