It's a vexed question.
I drove an Austin Healey 3000 for many years without a roll bar -- never gave it a thought. We were able to drive with just lap belts back then, and even today I'd rather a lap belt than a lap/sash belt in an open car without a roll bar. It may be fanciful but I think that if the car were to roll, I'd like to be able to throw myself down and sideways into the centre of the car and not be pinned upright by the shoulder strap. Whether you'd have time to react, I don't know, and there'd doubtless be any number of experts who would argue against my point, but -- just my two cents...
With Cobras you have the choice of going from nothing to a full race type cage with bracing everywhere, but even then, without arm restraints your arm could flop out and be injured by the rolling car. So without building something grotesque, you have to accept that an open car carries an inherent risk of greater injury that a tin-top should things go pear shaped.
Some choose a full width bar with two rear braces and I think that's as far as you want to go. It's a bit like riding a motorcycle. You ride as carefully as you can, you become a little paranoid and treat other road users as dangers, you accept that what you're doing is dangerous to an extent -- but if all this becomes too much and you become fearful of riding, then you're better off just getting a car. Same with open sports cars -- accept their safety limitations, enjoy the good days, put up with the bad weather, but if it all becomes too much, go buy an SUV.
If you go hoop style with your roll bars you have to decide one or two. Wives and girlfriends rightly think they deserve a bar too so you see more twin setups than singles. Personally I like just the one. For safety/ club racing purposes the accepted dimensions are that the top of the bar must be at the upper end of an imaginary line drawn from the front of the body at its highest point above the radiator opening clearing the driver's head, then on to the top of the roll bar. This invariably means that, while the bar should then protect the driver in the event of a rollover (assuming of course that it is sturdily made, mounted and braced) it ends up being too high and looks odd or a case of overkill for normal road use. And then it should be padded!
The upshot of all this is that most guys sensibly avoid the cosmetic approach where a bar is not braced, or worse one leg of the hoop is mounted down onto the frame while the other is simply rivetted onto the fibreglass of the body. Total waste of time! Similarly any bar that does not rise higher than the driver's head not only looks faintly ridiculous but is next to worthless and is only adding unnecessary weight to the car for no discernible purpose.
So, a full width bar, made of suitably strong material, and
braced, either two rearward facing with a diagonal, one forward facing, or both, is about as far as you want to go for normal road use. Two hoops, to keep your passenger happy are fine.
My Arntz is fitted with the original single hoop, with the unusual slightly stretched inner leg and forward facing brace down to the passenger's footwell. It's very strongly built, as seems to be the case with all aspects of the Arntz cars, and importantly the bar forms a frame well clear of the top of my head. Any roll bar where, from a following car, you cannot see daylight between the driver's head and the inside of the bar, is simply too low.
I have an old Mercedes Benz 500SL which has a recessed roll bar that would pop up in a fraction of a second should the computer decide that we're going over! The windscreen frame is also built to withstand the force of landing upside down. I don't know if Miatas are similarly constructed.
However, having said all that, if some kind soul offered me my great old Healey back to drive for the rest of my days, I'd happily do so. Similarly, if I ever build another Cobra, it would be a locally manufactured one, the
Absolute Pace - Kit Car Manufacturer of Cobra & GT40 Replica's and other modern Sportscar kits (formally Race Car Replicas Australia) and it would be built in "road" style, without scoop, side pipes or roll bar.
If you want a roll bar, fit one that looks the part but is also going to go some way to saving your noggin if called upon to do so. Cosmetic add ons are clearly silly.