In a truly capitalist society, even going 100% cash free and doing all commerce electronically won't stop crime.
Take high level drug dealing, for instance. How does one move $500k in meth without being tracked and registered when there's no more untraceable cash?
Answer: Art. Prices in art are fluid. There's no material expenditure chain. It's not like the artist is building cars, with every bolt, gear and spring accounted for. Seven or eight dollars in paint or canvas could be sold for twenty dollars or a half million dollars.
So, every quarter ton of meth being sold out the back door looks like a gaudy painting being sold to a "collector" out the front door. The DEA and IRS will think it's all legitimate.