Even if it was possible to create new wallets for every transaction, wouldn't you want to spend it somehow? Then, the "flow" of cash from a subset of wallets at the same time indicates _something_.
Once this system had a few users, the difficulty of tracing any particular wallet 'owner' would be significant.
I suspect that "random" in this instance would have to be very carefully defined, as a lot of signals only become more apparent (to the human eye) when cloaked with the right type of noise.