I would consider myself an experienced player. I have been playing League on and off for about 3-4 years and I play with a locked screen about 90% of the time when in game.
It is quite possible that the reason I have stuck with using a locked screen for so long is because of habit and fear of change, but I can't deny that I find there to be several benefits to using it.
The main benefit to me is reliably following my champion and not having to worry about moving the screen. I'm quite a paranoid player so I would hate to accidentally walk into a fight while my camera is off elsewhere, or having to mess around with adjusting the screen because a team fight has moved out of the view of the camera.
However, that doesn't mean that a locked screen should be used all the time. The other 10% of the game is unlocking to look at certain events, typically for scouting purposes. For example; I will regularly unlock to watch team fights I am not involved in(this is so I can see the general performance of the team
and to see if it is possible for me to join the team and help/pick off survivors). Another example would be to watch the enemy team fight Dragon/Baron, to see if it is possible to steal or engage on their possibly weakened team.
Other possible reasons to unlock would be for general vision of the game and when using long range/global ultimates.
I really wouldn't advise anyone to play locked permanently, as it makes the above benefits very difficult/impossible.
In conclusion, I play with a locked screen because I find it removes the need to constantly re-position the camera and because I have gotten used to it, but also unlock the screen to benefit from scouting and using vision to make important decisions throughout the game.