It is possible to remove the agent's access to unassigned tickets views. In order to do accomplish this, you'll have to modify the agents' role (e.g. the Staff role) so that the setting What kind of tickets can this agent access? is set to Assigned to this agent only.
This prevents agents from being able to view or search for tickets that are not assigned to them. The agent will still be able to grab tickets with the Playlist button despite not being able to see the tickets.
However, this solution also prevents the agent from seeing historical tickets assigned to other agents. This may not be practical depending on your team's workflow. Our team is working on some changes that will make it harder for agents to cherry pick tickets in the upcoming version 3.0.
Here's a sample role with restricted access: