Yes. The only way to tackle illegal activities like tax evasion, drug dealing, and money laundering is to reduce the use of cash as far as possible.
So something that has legitimately been used in everyday life by ordinary people for thousands of years has to be scrapped, just because of people who abuse it?
Is the only way to stop house fires for us to ban matches? The only way to stop bike thefts is to ban people from owning bikes?
Be careful what you wish for. Once cash is gone completely, the government will seek to exploit the fact that they can know everything you buy. Currently, they can only see how much you spent in total with one retailer, but I can well see how systems will get a little more sophisticated so that all of your purchases can be itemised.
Those old enough to remember ration books will see the modern digital equivalent, whereby you're either charged a much higher rate of tax on 'bad' items or outright forbidden from buying them outright. This could easily be linked to NHS records of your weight. No longer any need for your GP to ask you how much you drink or smoke, or how healthy your diet is, as all your purchases are already monitored and recorded and they can already see your individual 'scores'.
Suppose you're pregnant and are trying to buy alcohol as a present for somebody else, that could be banned too, maybe with an automatic email sent to your GP to report you. Plus, if you're 'found out' buying formula milk and have not had it 'OK'd' by a HCP that you're certified as unable to breastfeed - that could be something else that they tax heavily or ban outright until you have official 'permission'.
None of this is very much of a jump at all - China is already doing pretty much exactly this. I can't understand why people are so desperate to see the option of cash, alongside other digital methods, eliminated.