> I mean, most banks don't require ID to make a deposit.

Due to money laundering regulations, that isn't really true anymore. Most banks straight up won't take cash deposits into someone else's account, identification or not. Other means (ACH, etc.) require KYC from the originating institution. I'm not sure about secure funds like a money order, but I'm guessing they'd be subject to some sort of verification as well.

At my bank, if you fill out a deposit bag with the account number and put in cash, you can drop it in the deposit slot and it shows up in the account. There is no verification that you own the account, beyond knowledge of the account number.

Sure, if the original contract had a clause that said “anyone can come add money to this and if they do, go ahead and extend it under my name” then this would be entirely reasonable. It seems that clause doesn’t exist here or at least GoDaddy isn’t required to exercise it.

This hasn't been true in the UK for at least a few years now