I too can see a problem with younger kids (4-12 or thereabouts) as for the most part they can get in the way real easily. Younger than that & they tend to be in a stroller which, providing weather isn't too hot or cold, isn't a big deal assuming that they aren't crying/fussing (I remember when my kids were young, sometimes they just HAD to come where we were going for various reasons). In that case (kids in strollers/very young kids) the auctioneer should say something in the beginning that they're welcome as long as they don't cause a disturbance to others. If they do then they'll have to leave. Said at the beginning hopefully it won't cause a problem later if the kid does start to cry.
13-18 though, not allowing them there I feel is wrong. As has been mentioned, some of them are there learning a useful skill. Beyond the obvious of locker buying, there is learning to read other people, how to quickly evaluate a proposition (when the door goes up), bargaining, learning to deal with other adults in semi stressful situations, etc. Learning that at an early age would have given me a nice step up in my 20s when I was just starting out as an adult on my own. Also as it is summer & school is out, my kids (14 & 16) are a big part of my labor force if I do win a locker. They have a great time looking through things for the first time (& have gotten quite an education when they ran across the tote full of sex toys....
) & helping load up the truck. They've even got a friend or two to volunteer to help out with the offer of picking out some small things from the locker (you can easily see who's read Tom Sawyer & who hasn't....
). For me, having them there is priceless. Being away from the house & away from the things that cause confrontations (phone, tv, rooms not picked up, etc) we have these great conversations while working together, am able to impart some valuable life lessons in easy to understand ways (even though we're going to make a lot from this locker we can't go buy something for us or go out to eat right now because we haven't sold any of it yet, try to keep your 'stuff' to a minimum, etc).
So if places want to ban children, I'm somewhat ok with 12 & under. However there are many legitimate reasons that teenagers have to be there (with a parent).