The short answer is: They do! But it is not a durable solution. More have to be lifted out of the most heavily strained areas and get resettled in more stable countries.
4 out of 5 refugees are in a neighbour country. This means that the majority of Syrian refugees are stying in Turkey, Jordan and Lebanon, while modt of the Afghans refugees are in Pakistan and Iran. Uganda is housing most of the refugees from South Sudan. This puts an enormous pressure on countries that already has enough problems with their own conflicts and with feeding their own population. The global society does far from enough to help these host nations; not much happens after the official speeches and promises of "more help in the neighbour countries".
The developing countries carry the large burden of the world's refugees. Only 16% of the refugees are in developed areas, and only 14% of the refugees in the world came to Europe in 2018. Denmark took very few of these, measured by inhabitants or economy (see more under Does Denmark receive many on a world scale?)
DENMARK VERSUS LEBANON 2014
One third of the refugees in the world live in the the poorest countries like Bangladesh, Chad, DRC, Ethiopia, Sudan, South Sudan, Tnazania, Uganda and Yemen. These countries only account for 13% of the world's population and only 1.25% of the global GDP, yet they are hosting 33% of the refugee population.
Many refugees spend their lives and maybe even generations in large, permanent refugee camps such as Dadaab in Kenya, Zaatari in Jordan and the now bombed Yarmouk in Damascus. UNHCR has endless waiting lists in their resettlement program, beacuse too few countries participate and receives far too few.
10 COUNTRIES HOUSING THE LARGEST AMOUNTS OF REFUGEES 2018
Many of the refugees who arrive in Denmark have also tried to live in neighbour countries for a period. To flee to another continent is not the first thought that comes to people. Moreover, it is very expensive to get to Europe and the journey usually means risking your life.
In Turkey, only 10% of the Syrian refugees are living in refugee camps. The rest are trying to survive as best they can – thay have no right to work, and the children have no access to school. Tutkey is not safe either, refugees are being deported over the border back to Syria and Iran, and it is not possible to apply for asylum in Turkey – at most, you can be temporarily accommodated in a refugee camp. If Europe had taken a similar amount proportionally as Turkey, 26 mio would have arrived to Europe.