One hypothesis for the cause of LLSVPs is that they are thermochemical piles caused by accumulation of subducted oceanic crust at the CMB. However, although subducted oceanic crust is denser than its surroundings, it was unclear whether thin oceanic crust could provide enough negative buoyancy to overcome viscous stresses that act to stir the crust into the mantle. Our results find that viscous forces caused by mantle plume regions are stronger than the negative buoyancy of subducted oceanic crust, so the crust is easily stirred into the background mantle. A small amount of crustal material may collect at the base of plumes, but it is sufficiently entrained away into the plume and does not accumulate into larger-scale thermochemical structures. Therefore, it is difficult for a thin subducted oceanic crust (~6 km) to accumulate into large piles at the CMB with the same size as LLSVPs.