Even if it's a fully caged car?Just because you are not allowed to go on track without it (at least not in Sweden).
Just like @Brayden_connolly says it depends on class and event. You can race an open Miata for instance (with roll bar). However, plexi/plastic windshields are not allowed, but on rear and side windows it is ok. I've had my car on trackdays on hot summer days and they didn't care about my open top, but the side windows had to be winded up, so It depends much on what track you are at. Roll cage/bar is not mandatory for trackdays but for competition it is absolutely required. Noice restrictions has also become harder at some Swedish tracks. -If you are louder than 95 Db they'll kick you out.Even if it's a fully caged car?
And even though they are "open" cars they still have to retain the hoop/halo/targa? bar when the windshield and top are gone.There is a little history behind this. In Europe, the FIA had production GT categories that the X1/9 fit into nicely. In these classes the X1/9 qualified as a coupe/GT and removal of the roof/windscreen structure was not permitted. The builders like Dallara and Filipinetti, who raced these cars successfully in the early years build many of them as customer cars. They were the pattern that other builders copied. In FIA classification, which is used for most road racing and hill climbs in Europe, removing the windshield moved the X1/9 all the way up into the 'sports prototype' classifications. Here, purpose built sports racers were the norm. Then incorporated monocoque construction and double wishbone suspension. The heavy, production unibody, strut chassis, X1/9 would have never been competitive.
In the US, the X1/9 fit nicely into the "Production" road racing category where production based sports cars (2 seaters with open tops) were the norm. Austin-Healy Sprites, MG Midgets/Sprigets, MGBs, various Triumphs, and other little British sports cars were very popular. SCCA, with a ruleset that was independent of the FIA, permitted "open" cars to remove the windshields, this a spinoff from some early British sports cars that had folding windshields, that were a noticeable aerodynamic advantage. Thus the X1/9 fell under the F and G Production class rules set and therefore had their windshields removed.
X1/9s can also compete in the old GT5 and now GTL classes of the "Production GT" ruleset. Here the rules are somewhat less restrictive than the Production classes but a GT is defined as a coupe or sedan and thus the X's roof must be retained.
And even though they are "open" cars they still have to retain the hoop/halo/targa? bar when the windshield and top are gone.
Interestingly, in Canada - we were not allowed to use a roof even if it was bolted on (for regional road racing, but Solo 1&2 allowed it). The only way to have a roof would be to fabricate it out of metal and weld it onto the car. A windshield was optional. I cut mine out after it cracked. The rules require a full cage if you have a windshield, but a low front hoop is acceptable if no windshield. So mine had a full cage and no windshield but didn't look too bad.
In what way would the windshield help in case of rolling? Wouldn't it bend and break very easy if rolling? To me the Targa bar seems to be the most important part and would take more or less 100% from an impact. But is it strong enough? It would be interesting to see pictures of a X1/9 after rolling. -I am afraid it would look like a pancake.If I were to run a Production class X1/9 today, without the windshield, it would have a full cage.
Most people think of a roll bar's function in a rollover on flat ground and its primary purpose is exactly that. But racing isn't a perfect world and I have seen cars get launched up and over other cars, cars roll on armco barriers, or submarine under barriers. In those scenarios the driver would be exposed to a physical impact. A full cage would prevent most of these risks.
I can personally attest to the strength of the X's targa bar. I had a rather dramatic rollover incident in my very first X1/9. The car landed hard on the top and slid approximately 75 feet upside down. The rear window didn't break. The car literally saved my life. Had a been in a traditional convertible, I would have liked been fatally injured.