In this situation, the ultra sharp cantilever tip might not slide successfully up onto oxide stripe. Instead it might break off. This ruins the instrument's near atomic resolution (requiring us to buy and install a new micro machined cantilever assembly!).
There would also be problems if we were measuring the shape of a soft material, such as a strand of DNA. In this case the sharp tip might just pull its way right through the strand, giving us no information about its shape.
What is required is an alternate method of operating the instrument known as "Dynamic Force" AFM.