Yeah not all shelters are this way.
Why don't you look up some rescue groups in your area and help out with them! I know some shelters will also only let minors volunteer if their parents are there with them everytime!
It is a shame, but I used to work at one shelter and I always felt worried for the animals, and for the kids, kids just don't pay enough attention (no not all kids).
One of the rescue groups I work with has a lot of young volunteers that come in to clean cages etc.
Now I GUESS that I need a bigger sign or something, but they were cleaning my former fosters cage (zene) and some approx 12 year old girl was holding her, (even though the sign says she does NOT like to be held). So, I'm like "uhg, she's gonna jump and get loose, or the girl is gonna get sratched." no more than a second later Zene makes her move, the kid almost looses her but luckey is standing close enough to her cage that she can turn and just have her jump in there.
So I had a nice little talk with that (child).