The amounts that airlines have to pay for their fuel won't come down.
The landing fees at airports won't come down.
The fees paid to companies like Swissair for baggage handling and passenger boarding services won't come down.
The wages to be paid to pilots (many of whom are contract workers, rather than employees and so who can simply be laid off if flights are cancelled) won't come down.
So if airlines continue to operate flights, but with lower fares charged to their passengers, they'll end up making a loss.
If Covid-19 becomes a pandemic, many airlines will end up going bust. So, in readiness for the financial problems that they might face in the future, all airlines will be looking to 'tighten their belts'. The very last thing that they'll want to do now is to operate loss-making flights.