Yes a fully caged car is meant to have an occupant inside that is protected. Think, "A cage doesn't have impact absorbing crumple zones." As a result if your head/neck/body isn't protected with a helmet, ideally a neck restraint, and a proper containment seat, you've reduced your body's ability to absorb the impact.
Physica dictates opposite and equal reaction. In a street car without cage, the car has built in crumple zones that absorb impact (negating the force applied from a crash). A roll cage simply does not crumple (assuming a properly constructed cage of appropriate materials).
A street car can have a "half cage" roll bar in place. As long as your head is clear of the top bar of the cage (including when wearing a helmet), while you are belted in, you should be fine in the event of a collision on the street.
It is imperative that your head clear the top hoop of the roll bar when installed and you're wearing a helmet. Most sanctioning bodies use the "broomstick test". Can you freely insert a broomstick between the top of your helmet and the roll bar hoop when belted into place. If you don't clear the top hoop, than a roll over can result in the aforementioned spinal compression damage. The bar absorbs the roll over, you stay belted in the seat.
-
Remember there really aren't half measures here. If you do not wish to install a roll bar, then opt for sport seats that provide more side bolstering and use your factory 3-point belts. If you need more tension that is easy. Pull the belt all the way out to lock the ratchet and then pull it tight over your hips and chest as the belt reels in. That will lock it firmly into place, yet still allow it to function as intended in the event of a collision.