Why now? Answer me this, and I will concede.
When a person is put into a tough situation, he doesn't simply say, "Too tough. Lets back out." There is a struggling period.
People of Dressrosa were trying to run as much as they could for quite a while now. Fighting each other. Trying to capture the starred people.
Pretty much acting like a drowning person would. Doing whatever you can until you meet the end.
Of course, not everyone has a will as strong as Shounen protagonists. At some point in time, people just lose hope that they have any chance of survival.
It is usually different for people based on how strong willed they are.
If you notice carefully, not everyone had left hope. While some were just sitting it out, grandma was still hoping for her granddaughter to live, while the others were trying their best to escape while at the same time helping others.
Now is as good a time as any for some of the people to lose hope.
Most people are not aware of Doflamingo Family being almost completely taken out.
Some people saw Doflamingo being in Central District. These same people also saw Pica getting taken out who was again present near the Central District.
People who are losing hope are those at the edges. They aren't really aware that the situation has changed so much.
King Riku's speech was supposed to inform the entire country that there is still hope. That Doflamingo's empire has already shattered and his bones are on the way.