Think about it. Race cars are sedans, the entire cage is built inside the vehicle, trapped by the top. Some parts tied to the frame and some to the body are acceptable - it can't really go anywhere.
But - Jeep tops come off - fabric, glass, or no top at all. That's a different story.
Formula cars and the like don't use add-on roll cages, the entire car is the cage.
A cage tied to the frame? Seats are tied to the body, you are inside the body - even if you tie them to the cage on runners the floor, dash, sides etc is underneath and around you. If the body separates from the frame (look at what holds them together - flimsey little mounts) the body lifts up or moves sideways, you get trapped between the body and cage. They make gopher traps like that - visit a Walmart.
Take a walk around a junkyard - Notice how many frame type cars that were crashed have broken body mounts. That was one big reason they went Unibody!
Best way - design a safety capsule that stays together. If the frame goes one way, and your capsule goes the other - who cares as long as you live!
Interesting - do a little research - DOM - Drawn Over Mandrel - it's rounder than ERW - and more brittle - the drawing process work hardens it. It's intended to be used for hydraulic cylinders where round is critical 'cause it has a piston going through it. It's the same steel as ERW, just harder because of the work hardening. Try bending both - the DOM is much harder to bend - even though it's slightly thinner.
Now when you bend already work hardened DOM it work hardens even more - creating stress lines in a different direction than the original stress lines - crosshatch style. Oops - too much work hardening causes tiny stress CRACKS. Now it can shatter easier - like tempered glass.
I'd rather have it bend a little than shatter. Try bending some DOM - then acid dip it - then look at it close with a magnifying glass - see the tiny cracks like a crazed windshield?
Do the same with ERW --- you decide which you'd rather stake your life on.
Proper design, or one little extra brace, or good corner gussets, or internal stubs are far more important strength-wise than the small difference in possible dubious strength due to work hardening.
Stay safe, stay alive!