How about a lower rank than member, we'll call it "recruit" for sake of brevity, that has only limited access to guild amenities. Including member-only chests. This way, at least they would have to earn some officer's trust in order to gain access.
Doubt it'd stop every instance of chest-theft, but it'd stop some. Most would probably leave that guild as soon as they found out they'd have to earn full member status and go find an easier mark. Logging wouldn't stop the issue, just make it easier to catch the thieves. And there's not much a guild can do other than blacklist them, and warn other guilds to do the same. It'd be up to Turbine GMs to update the TOS and then enforce the rules against caught thieves. Because currently I don't think there's anything in there which prohibits taking from a guild chest that was filled for the express purpose of guild members taking from it.
Of course, knight77504's method of having a "fake" account added which serves as the guild "chest" accessible only to worthy officers/leader, is probably the safest method you have currently.