It's interesting to me that North American and Asian-designed convertibles generally don't have rollover protection, while European-designed convertibles generally do. One of the methods used is called ROPS, whereby a bar (or bars) deploy(s) at the onset of rollover. If you see access panels behind the rearmost occupants, they may be hiding a ROPS system. One of the major manufacturers, ISE, showed us this video over 10 years ago. Their video was higher quality, but you get the idea:
The one in the video is a swing up roll hoop, which was an early design. Most of the systems used today are smaller, cheaper, and deploy vertically, like a giant steel cassette being ejected from a car stereo (or an 8-track if you're old enough to remember).

It's unfortunate, but not surprising, that many OEMs don't spend the extra $$. I'm amazed, however, that government bodies like NHTSA don't require convertibles to pass some sort of occupant protection standard during rollovers.

On a side note -- the seats that have integral shoulder belts have such substantial structure to react the belt loads that the seat back actually provides some measure of front seat occupant protection during a rollover . . . hmm.

 

Important point. I doubt manufacturers of that padding test with an unhelmeted head. I'd do everything I could with the seating to try to minimize the possibility that my unprotected head came anywhere near the bar. Padded or not.

And the forces involved in a collision are unintuitively high. For an idea of a scenario that I doubt many of us would anticipate as we bolt down that seat in our garage, check out the helmet review written here

With video of the crash
and additional photos here. Sequence through all the photos for stills showing how the occupants get thrown around in the crash, and what happened to the seat mounts.