Even with IBIS turned off you may have jittering and other problems. That's one of the reasons why most cinema lenses also don't have IS.
Anything that makes sensors or optics move could be problematic on set.
Probably not: Cinema lenses don't have IS (or AF) because these lenses are used in very specific conditions, where IS is not needed and lens designs are already complex and expensive enough. Cinema lenses have a lot of moving lens groups, for focusing, zooming (if zoom-lens), and moving groups to counter focus/zoom breathing.
For IBIS (as well as for AF), the argument can again be made that it is not needed for cinematographic shooting. Some others can strongly benefit from it: vloggers, documentary, run&gun, etc.
The wobbling can probably be minimized by tuning the IBIS, i.e. tune it down if you mount a <24mm rectilinear lens; shouldn't be noticable on a gimbal and there should be an option to turn it off. I don't see a strong technical benefit for not having IBIS, while having it makes a camera more general purpose driving costs down.
Just my 2c.