Restrictions on camera mounting is growing - mainly from experience. Some clubs prohibit ANY external camera. Some prohibit external cameras on a suction cup (must be hard mounted or the GoPro adhesive). Some require a back-up leash.
I was out last week with PCA and they don't allow internal cameras on a suction cup. Too many past incidents. I know NJ BMWCCA requires a hard internal mount and a back-up leash that prevent the camera from reaching the driver or passenger.
Keep in mind that a back-up leash needs to be completely independent from the hard mount and be strong enough to be effective if the car makes contact at speed with something. 20 lbs. tensile strength isn't going to cut it.
Getting clocked by a camera and mount at sudden deceleration would not be fun - let alone it getting under the pedals.
And restricting timing devices (data acquisition) is nothing new. As noted above - its an insurance issue that affects the club's insurance and the liability of everyone else at the event. Putting tape over the display shouldn't be an issue at an HPDE (assuming the club allows that). Having students watch a timing/"Best Lap" display misses the point of why they are there. Do your data analysis at home - not at speed.