What advantages are there to playing with a locked camera?

Solution 1:

The key advantage of playing with locked camera is not having to mess with camera control. Especially for a new player, keeping track of your champion may get difficult in the middle of a hectic teamfight with lots of spell effects going on, particularly if you're playing a champion with lots of mobility. A locked camera means that your champion is always in the center of the screen, so keeping track of where you are isn't hard.

Solution 2:

I'm surprised nobody mentioned the spacebar.

If you are an experienced player I would advise against playing with a permanently locked camera, however that doesn't mean you shouldn't use the lock camera feature at all. Also if you feel comfortable with a constantly locked camera you can go ahead and use it. I know high diamond players that play with a permalocked camera.

Now in general I'd recommend using the spacebar in order to lock and unlock the camera. By default the spacebar locks your camera temporarily while you hold it down and unlocks it as soon as you release the key. This allows you to look around whenever you want and if you get involved in a messy teamfight you can just hit down space in order to lock the camera and get a better overview of the fight.

Space as a key comes especially handy since you won't use your thumb for any other key and the default permanent Lock/Unlock button is on either Z or Y (depending on your Keyboard layout).

Although using Space to freely switch between locked and free camera is extremely effective you still have to keep in mind that changing your camera behavior is a huge shift in your playstyle and you should practice it first.

Solution 3:

If you play with the camera always locked, you'd lose awareness as for trying to see what's happening below/behind your character. Also it's annoying when you have dashing champions around OR if you're using one, because it won't make you easy to aim properly with your mouse, specially if it's about skillshots WHILE you're moving with the camera together.

While I'm playing with the camera unlocked, I use the spacebar so that I can be aware of where am I walking.

The "camera locked" feature is only for people who don't want to get lost in the map (or messing around with the camera as Yuuki said) when they barely start playing these kind of games. Once they develop some experience and realize (from experienced people), they'd release the camera eventually and get used to the space bar whenever they feel lost.