Although, I'm a huge fan of transparency - strictly read-only -, this feature scares me. It kind of allows the customer to change the backlog without having a proper discussion with the team or organization.
Let's say I'm a small company owner who has a contract with the customer and a budget to keep. In the contract, I agreed on a set of features I'm going to deliver and my customer is allowed to see my progress which is completely fine and a good way of maintaining business relationships. The business situation of my customer can change, and he comes to me for changing our agreement. We have a discussion - because of the read-only access - , change in the contract and live goes on.
If the customer has write access to the backlog, this discussion is pointless from his point of view and I became his slave who has to be able to react on any changes - it is a resource allocation nightmare - and I have to keep my eye on my own backlog and look for changes. This is a sort of micro management on a different level.
So, I see the following issues: contracts, resource allocation, project planning, and need for a notification feature.