liquidmetal: The problem with rail shooters currently is "the medium".
Original rail shooters like Virtua Cop or House of the dead were arcade cabinets in which you held a plastic pistol as controller.
In that setting, it actually does make sense to remove the player's ability to walk since physically, the player is standing in front of a screen and genuinely aiming at the screen with a dedicated controller.
The pace of the action is decided through the level design. You need to "learn by heart" where the enemies will come from and aim accurately at this portion of the screen on the various movements phase.
There were rail shooters also back in the SNES days where you had a sort of bazooka acting as a controller. Scrolling/movement was also taken out of your hands since the basic gameplay was about aiming.
On actual PC and consoles it is harder to give back that physical aiming feeling (aiming with a cursor that is dependent on your mouse or thumbstick just doesn't give back the same feeling and reward of physical aim).