For one, it makes it harder to see around you in general. In a specific example regarding ADCs, think of Varus. His Q is a skill shot that charges in order to reach max range and damage. With a locked screen, it is very hard to aim the arrow at max range. Keeping the screen unlocked allows you to see just how far it can really go. Another con is purple side in general. If you play in bot lane on purple side, your vision is seriously gimped with a locked screen due to the UI (your spell bar, your inventory, the minimap, etc) and it makes your life a lot harder.
The only pro I can think of with locked screen is that it makes it impossible to lose track of your champion, especially in clustered team fights. That camera stays locked on and you will always know where you are, whereas in unlocked (ESPECIALLY if you aren't used to it) you might lose track of your champion's visual location since your screen might go one direction and your champion another.
If you're used to playing locked, keep your screen unlocked but every now and again, just to feel a little at home, press or hold the spacebar. This will instantly bring the camera to your champion as if it had been locked. If you hold the spacebar, it will "lock" your camera until you let go of the spacebar again. I seriously recommend learning to play with an unlocked screen. Once you get used to it, it will make your life a lot easier.
Hope this helps!