A system could create, manage and automate a 'cloud' of several hundred wallets, all shifting small amounts of money around at random intervals. When the owner decided to make a particular payment, he could set a target sum to be accumulated by a single wallet, and within a few hours (or days), make payment from there.
Once this system had a few users, the difficulty of tracing any particular wallet 'owner' would be significant.
If these nodes aren't shared between users then you're not really getting anything more than minor obfuscation. If they are shared then you in fact have a third party cloudbank that hopefully is trustworthy and the money cloud aspect is a distraction that doesn't provide any benefits.
all shifting small amounts of money around at random intervals
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.
Once this system had a few users, the difficulty of tracing any particular wallet 'owner' would be significant.