For a setup where travel needs to change direction without going off course (as in a rotating monitor that rotates within a fixed path) a swivel caster would be a serious error. When a swivel caster changes direction the wheel needs to pivot around IT'S pivot point which requires it to move perpendicular to the desired travel for a brief moment.
For an example look at the front casters on a shopping cart (trolley if you're from somewhere with less American English.) Watch what the front end of the cart does if you try to switch from forward travel to backwards travel, the front of the cart will shift to the side while you change directions. Now imagine that the cart cannot shift to the side, like it was pinned in the center, or trapped between guides, it will start to turn the caster and then drag it or make it wobble.
The drawback to a fixed caster is that if you don't get it aligned right (there is some room for error) it may drag as well, but lining them up with the direction of travel is not that difficult.
In theatre we frequently make large parts of the stage into turntables which act much the same as what we want a rotating monitor to. Imagine a 30' (that's foot not inch) monitor rotating under motor power and hitting it's desired position with less than 1/2 inch of error and you'll picture what I'm talking about. We use fixed casters to accomplish this, swivels would bind.
Not trying to sound all braggy and know-it-all, I just want you to know why I'm saying I know the answer and trust that I've tried and seen the results of both options.
AND fixed casters are usually cheaper.