I think it improves the efficiency. Normally the heat radiates in all directions, including towards the wall and up towards the ceiling. We really don't need to heat the ceiling, or that wall.
The radiator cover will direct the heat into the center of the room before it rises to the ceiling. I think a radiator cover with sheet of galvanized steel in the rear will be even more efficient, especially if it is curved and directs the heat into the room.
Most radiator covers I've seen are open in the back allowing a good portion of the heat to go straight up the ceiling.
Hot air rises right?
Which means as soon as it clears whatever obstruction is keeping it from rising, it will rise, just as you indicated with the open back.
So there really isn't a "direct it to the center of the room", it will move it slightly forward until it clears the obstruction.
It addition it may feel warmer near the radiator because the air flow isn't allowing as much heat to be transferred to the (obstructed)passing air, so the surface temp of the radiator may be higher.
The only thing that makes sense is the metal panel at the back, that would promote better airflow across the radiator(IMO).
I'm not a heating expert, just have enough understanding of this to be dangerous.
To me it seems the best design would be open at the bottom for cold air to enter, and open as much as possible at the top to allow the heated air to escape. If you choose to put a solid top on it, I would omit the top rail of the cabinet to allow the air to move more freely.
Here's just one clip from a site I found when I did a google search on "radiator cover design considerations", looks like some of what I think is correct, some may not be...
Lots of concerns/considerations
Most radiator enclosures result in decreased output. All enclosures have a significant effect on HOW the radiator liberates its heat.
All diminish the radiant portion of the output. The method of construction determines how much the convective portion is enhanced to overcome this. You essentially want to turn a radiator into a convector.
Below from enclosure studies where the quantity of condensate produced by a steam radiator painted black was used to determine differences in output. Water radiators AT HIGH TEMPERATURE (around 180°) are said to have nearly identical characteristics when covered.
Manufactured metal covers reduce the output by about 15%.
The most efficient typical enclosure leaves an open "slot" about 5" high at the bottom of the radiator. The top contains a grille the same depth and length as the radiator itself. TOP AND FRONT PLACED 2½" from the corresponding faces of the radiator. Placement of side panels (solid) has little or no effect. About 2/3 of the grille should be open. This type of enclosure results in about an 8% reduction.
Output can be INCREASED if you do not use a top and instead cover the front and sides. Again, leave an OPEN slot at the bottom AT LEAST 1/5 the height of a tall radiator or 1/3 the height of a shorter radiator. Taller is better regarding the size of this slot.
A TOP ONLY "cover" should not be installed directly on top of the radiator. It should be at least 3" above the radiator. If the shelf only projects to the mid-line of the radiator it has no affect when 3" or higher. If shelf projects to the front edge of the radiator try to keep it 4" or move above the radiator.
Low "window-type" radiators were ALREADY designed to enhance convection. The output reduction effect is MAGNIFIED when covering low radiators. Generally output will be reduced by AT LEAST 25%.
In general, use the 2½" distance away from front and top and try to keep the area of the outlet larger than the inlet.
EFFECTS ON COMFORT:
Increased output does not necessarily translate to increased comfort and vice-versa. As all enclosures eliminate much of the radiant output there is a corresponding increase in convective output with those that are well-designed. Higher convection usually translates to higher temperature stratification in the space. So, while the "open top" example may be producing more heat, much of this is just zooming to the ceiling with cold air being pulled across the floor with increased velocity.
It is possible to design an enclosure to counter this effect--it essentially tries to "project" the convection into the room instead of letting it rise to the ceiling. "With a well-designed enclosure having a large free area of grille work at front and ends with a solid top and a back carried down to the floor, a tubular cast iron radiator may operate to produce higher useful temperatures in the living zone below the breathing line and lower temperatures in the upper part of the room for a given breathing line temperature and at the same time condense less steam than the same bare radiator."
Again, these studies are either with steam or very hot water. With modern control, insulation and weatherization, old water radiators generally operate at MUCH lower temperature than their design. As the temperature of the radiator decreases so does output, BUT convection decreases more rapidly than radiation. Temperature stratification decreases as well. This contributes GREATLY to the comfort of these old systems and covering the radiators negates this benefit. When old oversized water radiators are controlled proportionally, many will claim that they approach radiant floor comfort.
Because iron radiators are now typically quite oversized, a radiator cover (even one poorly designed) most likely won't result in not enough heat. BUT in a simple unzoned system you may well upset the temperature balance compared to other uncovered radiators in different rooms. The rooms with uncovered radiators may now overheat.
If at all possible I would try NOT to enclose the radiators. A good cleaning (a pressure washer with zero-degree nozzle works great) and repainting can do wonders. Modern "bronzing" can be extremely attractive.
Modern "bronzing" is NOT the same as old bronzing which actually contained metal particles. Modern bronzing is actually mica in most colors. As best as I can determine, "paint" made of mica powder and linseed oil has an emissivity only slightly lower than standard paint, so the effect on radiant output is very small.