Just make access like mailbox, security setting to withdraw, but anyone with access to the house can deposit
The problem with having it so you can't elect to have a wall safe DEPOSIT ONLY is that ANYONE with access to the safe can take out money intended for the house owner only. You can have more than ONE wall safe in a house, so there is no reason ONE of them cannot be set to deposit only (if the option was there) and others with settings similar to the mail box settings of withdraw/deposit.
I know I am currently coowned/friended access to mailboxes in game due to shard transfer issues, and yes, I can deposit items to transfer etc, but I can also withdraw and often I see 'other' players deposited items and if I wanted to I could 'take' them as I have access. In the case of auction houses, and guilds there is no way I would 'trust' that everyone is as honest as me, nor as a person running auctions would I want to 'trust' all the people buying etc. You currently have to 'trust' that if you are coowned to a mail box that all other co-owners are people whom YOU would trust, and you have no control over who another house holder gives that access too.
You just need the wall safes to have ONE addional security setting of 'public' (in addition to friends, coowners, guild etc) and then give the safes a toggle to make them:
DEPOSIT ONLY
WITHDRAW & DEPOSIT
The fact that the wall safes rely on 'access' to the house to be able to use them means that the owner of the house has to physically 'add' the person to their house friend list instead of having a wall safe that anyone can use without the need to be 'accessed'.
Just a really bad design imo and a missed opportunity to make the object highly useful for guilds, auction houses etc.