It puzzles me why dust boots on dampers would be a safety issue

Some manufacturers use them and some do not.
The name is misleading for a start. They are air bellows which suck and blow dust and air in and out with each stroke of the damper.
They don't eliminate dust, just reduce the quantity which can settle and accumulate around the top seal of the damper. Accumulated debris around the seal can reduce its life. They eliminate splattering of the rods by flying particles.
Dust boots make it impossible to make a visual examination of the seal area for signs of accumulation or failure of the damper itself ie weeping of the seal. Such dampers should be replaced to the manufacturer's fixed schedule.
However pre-failure maintenance of any damper maintained to point of failure (our legal obligation) is less effective using visual inspection. (a potential safety issue in itself)
It is the seal which is the safety critical item not the dust boot. Failure of the seal has a safety consequence, failure of the dust boot has none (in fact it fails from new as it has designer apertures to let dust in.)
Splits or cracks simply increase the size of the apertures making the safety inspection itself more effective.
By rights the boots should be cut off for the inspection and then a decision made as to whether to replace them or not depending on the environment in which the car is used.
They may be an effective cover for chrome rods where splatter from salt or gravel covered roads is a well known damaging occurrence for example.
Safety is assured either by predetermined fixed damper changeout intervals or by testing and inspection to point of failure aided in part by pre-failure inspection of external damper seals.
Possibly boot life is a crude changeout indicator for the dampers provided by the manufacturers? Therefore changeout of dust boots is probably only a consideration if the owner follows a manufacturer's recommendations for fixed period changeout.
The legal requirement however is repair or changeout of dampers before point of failure not necessarily fixed period. (Imagine the red tape involved in enforcing fixed period maintenance !)