I don't think any amount of servers are going to help if they are completely unwilling to add an AFK kick or a proper queue time to get in to servers.

SE Solution and Probable Result:
Step 1: Add servers.
Step 2: More AFKs join servers and sit AFK for all of eternity.
Step 3: Thousands of people are still unable to join the "new" servers.

Solution and Probable Result:
Step 1: Add AFK kick after 30 minutes.
Step 2: Add more servers.
Step 3: Thousands of people can enjoy your game because they can actually log in to the "new" and old servers.