Why don't many convertibles have roll bars?
Most modern convertibles have roll bars.
They are deployed through the convertible top/bodywork/rear seats in a fraction of a second when sensors in the car detect that the cars pitch has transferred to a dangerous angle.
Some cars are offered with optional roll bars (think Mazda MX-5) that are attached to the frame of the vehicle and protrude out of the vehicle. When fitted, these roll bars replace the factory system, which is then either removed or deactivated. The obvious benefit to this addition of aftermarket rollover protection is the reduction in weight of the motors/electronic assembly associated with the OEM units.