Not sure if "mainly" means in terms of total value, number of transactions or people using it. If I would be to guess it would be total value.
Now, these guys might be biased, but to quote: "The EUR 500 note alone accounts for over 30% of the value of all banknotes in circulation (1)." (https://www.europol.europa.eu/media-press/newsroom/news/cash...).
That would suggest to me that at least 30% of the value of cash is used for "shady" stuff (I mean I don't know anybody that would use 500 eur bills).
The fact that cash would be used mostly for illegal activities by value (I don't know if it is really the case), does not imply that "people that use cash use if for illegal activities".
I do not pretend that I know either, to be honest.
That said, there is "For payments over €50, cards were the most frequently used payment method.", which means they primarily use cash below 50 EUR, and you cannot do much illegal purchases with 50 EUR, it is such a small amount.