It's good practice to get as much as you can from servo throw before gaining throw by mechanical means. Since a 1:1 setup can give you 35 degrees of throw each way with a proper mechanical setup, it's very rare that someone needs to go closer at the control surface than they have it at the servo.
And yes, there are disadvantages to moving the horn closer at the surface. First, it reduces your effective servo torque, which means you may not be able to actually get the throw in flight that you are setting up for. Second, it magnifies any slop in your system. Slop in your gears, all of your linkages, and any flex will add up. And third, less pushrod movement translates to less overall precision in your control system. If your servo doesn't center perfectly or if you are using analogs, you'll find that the plane starts to feel disconnected from your inputs. That's very frustrating when you want to fly with any degree of precision.