First, you're assuming your zines are even part of the collection. Are they? Other zine publishers may like that their work is being archived, so don't presume to speak for everyone.
Second, you're upset that people might make photocopies of zines and that just anyone could walk in and request these photocopies. Your attitude seems antithetical to the whole idea of zines in the first place. Most people began publishing zines using photocopiers and sold or gave them out to people they probably didn't know. How would this be so different?
Also, all these zines are going to be housed in Iowa. I don't live in Iowa, I live in the Pacific Northwest. I'm not going to drive to Iowa just to make photocopies (at 25 cents a page) of your hypothetical zine, which is probably not in their collection in the first place.
I don't know why you're so surprised that the physical copies of any zine are beyond the publisher's control. Why did you bother publishing zines if you didn't want anyone to read them? Perhaps you should have only distributed them to your secret circle of fan-closet friends and made them sign legally binding contracts stating what they could and couldn't do with the copies of your zine. Blood oaths and secret rites should be the only way the zine-worthy cabal may enter the caves of fandom at the U of I library!
You care so much about zines that you don't want anyone to be able to read them, and when they die out because of waning interest, you don't want there to have been any record of their existence. And now some other people collecting zines you didn't create or have any part in is getting you so twisted up that you're not going to do another zine as long as you live. Okay, fine.