Coronavirus shutdowns have quashed nearly all other common viruses
washingtonpost.comIf I read this right, the fact that coronavirus is still spreading quickly implies that it is much more infectious than other viruses. The methods we've undertaken work for viruses in general. They're just not good enough for this one.
It's not, strictly, enough to conclude that COVID-19 would have been much worse if not for the interventions, or that more strictness would have helped. But it does seem reasonable and likely.
I think they said it's spreading faster simply because no-one has had it before so there was zero immunity. Not because there's something inherently more infectious about this virus.
Obligatory XKCD (tweet): https://twitter.com/xkcd/status/1300507567974735875