The idea is that they will increase the reproductive rate. I didn't just mention that for the sake of mentioning it.
For a variety of reasons, living in a developed country is directly correlated with a lower reproductive rate. One idea behind immigration is that it brings in people with higher reproductive rates, increasing total reproduction rate by having sex with natives or other immigrants (it makes no different to governments. Tax payers don't have a color).
Nice logic bro.
I understand the sentiment you are expressing, and I agree. Systems that are built with an inherent dependence on growth or some other kind of forward momentum are inherently doomed to fail. Nothing can grow perpetually; the things that try are rightfully called cancers. Despite this, our social security structure, our healthcare structure, our government, and especially our economy have all been operating with this dependence for decades.
Low reproductive rates can't support an inherently cancerous participatory system, so immigrants are accepted into the country. This increases the size of the potential labor pool (making labor cheaper), dilutes native voter demographics (weakening their influence over their home country), and increases reproductive rates (which affects both other factors). This is good for established financial and political figures, but generally bad for the common person.
I realize now how much of a rant this turned into, so I'll try to be concise. When the immigration is regulated with background checks and specific qualifications, the immigration brings enormous benefit to the country. Examples include Indians in the UK and Chinese in the US. However, when immigration is
not regulated
and there are no policies for assimilation (as is the case in Europe right now), there is a failure of integration. Symptoms of integration failure include the formation of mono-ethnic neighborhoods and communities that are not welcoming of natives, low employment/employability, low education, increased poverty, increased crime, racial tension and increasing racism from all parties, and increased social and economic discrimination. This is the case for the majority of the descendants of slaves living in the US and for many muslims in the UK. Unfortunately, we're going to see these problems spread throughout mainland Europe in the immediate future as the refugee crisis progresses. It is truly a clusterfuck of "nice logic".
I hope no one thinks this is "xenophobic" or "racist". This is literally what happens when any group of people (immigrants) move to another country and become part of a minority group among the majority (natives).