It's all to avoid responsibility and blame. Something happens, hysterical parents throw fit, parent/reporter/boss you don't have a policy against that, or you used common sense/judgement. Well fu! Your job/career is over and we are suing/charging you. Or, Why, yes we have a ZERO TOLERANCE policy and I just say no to everything or pass the buck so no one can blame me. Well darn, I guess we'll have to blame rock'n'roll, drugs, or sex then.
You're probably right that that's why administrators like it, but I'm talking about public opinion, which is different. Tacit public support is a necessary ingredient here.