@ ora It is difficult to find data which are relevant to your question, for a few reasons. The majority of refugees are hosted by developing countries, not by developed ones. Of course this is because developed countries typically have strict immigration laws, which is what OP was criticizing. Studies of economic impact in places like Tanzania don't exactly indicate what the impact would be in Austria, or the UK, or the US. Additionally, what information does exist for refugee immigration in developed countries typically reflects a very low number of refugees in proportion to the native population, and often those refugees have a higher level of education. They are political refugees more than displaced civilian victims of a war. So again, the studies that exist are not relevant to the current situation.
I could quote studies of undocumented immigration into the US, but I fear you would then accuse me of hatemongering. I will explain to you why I would equate these situations and you can tell me whether it makes sense. Both populations arrive in greater numbers than standard immigration policy would allow. After all, this is one main reason for illegal immigration in the first place. In the case of these refugees, one can easily see that there are very large numbers of them, probably more than we would traditionally welcome. Also, both populations are relatively poor and uneducated. This is demonstrably the case with illegal immigration into the US, and in the case of the current refugees, it can easily be argued that those with money and influence were able to escape much earlier and are not now starving in refugee camps. Finally, any statistics which show government dependence for illegal aliens would certainly be multiplied by these refugees, who would not fear deportation when seeking government aid.
Spoiler alert: Studies of illegal immigration all point to a net negative to the receiving country when taking into account taxes paid by the immigrant. The cost of government aid in the form of housing, education, food assistance, etc trumps those taxes by a sizable margin. And those studies don't even attempt to calculate the cost of the crimes they commit.
And yes, you, the individual, orathaic, may feel that you have a duty to other humans. If you became MP orathaic, or Prime Minister orathaic, or American President orathaic, you could spend your private time and your private money doing that duty as you see it. However, you would have an obligation to those who elected you and whose tax money paid you to put their interests first. It is not the role of an elected official to decide when morality trumps the good of their people. In performing the duty of their office, the good of their people is the only concern that should be considered, and anything less is a breach of the oaths they took when they assumed that office.