Before one can being a discussion on the merits of free versus locked cameras, the terms must first be defined. Oh, sure, the distinction seems readily apparent just from their names, but these are concepts that originated in a bygone era, when technology was nowhere near as focused on the cinematic as it is now, nor did it have the potential to be so.
The first key point to remember is that "locked" does not mean "static," as in stationary. It instead, at least in this article, refers to a camera that is out of the player's control. You do not maneuver it. In contrast, a "free" camera is one that the player may manipulate, swinging it around their character.
The biggest question, though, is, "Why is this even a question?" Isn't the "free" camera preferable, now that we have the technology to affect it in all or most of our games? Player control and comfort is paramount, after all, no? Nine times out of ten, this is completely true. The free camera provides players with the tools they need to gauge jumps in a platformer, or to keep their enemies in sight in the heat of battle. If the argument is purely one of control, the "free" camera wins hands down, since it is open for manipulation, allowing the player to decide where they themselves are most comfortable.
That isn't to say that it comes free of issues. Programming an intelligent player-controlled camera can be a daunting task, evidenced by the multitude of games in which they aren't intelligent, and which suffer for that lack. The latter day Ninja Gaiden series comes to mind, in which the camera tends to lose sight of Ryu as he dashes to and fro about arenas, or runs up walls to outmaneuver his foes. That the player can control this camera is a moot point given the speed of combat in the title—swinging it around with the stick is unwieldy at best, in the heat of the moment, and the trigger devoted to snapping it around behind Ryu depends on him facing in a direction that actually makes sense, which, if the player can't see him, is not guaranteed. Part of becoming skilled at Ninja Gaiden is learning to read combat based on non-visual cues, or to fight without direct line of sight on Ryu.
This tends not to be an issue in games with a "locked" camera, since its position is either stationary or on rails tied to player position. The prevailing philosophy may be that this minor convenience is not an equitable trade-off for the potential inaccuracy such a camera begets, as well as the control it wrests from players, but there are extremely popular titles that prove it can work well. The Devil May Cry series comes to mind, as does Super Mario 3D Land on the 3DS. The latter, in particular, is a platformer from a fixed perspective, which works in part due to the 3D effect that the handheld provides. This allows players to gauge jumps into and out of the screen, movement into both the foreground and background. But perhaps the best example of a "locked" camera's modern day application comes from the God of War series.