Nope. Look at europe, walk through any major city, be it London, Geneva, Paris, Stockholm etc. You will see huge amounts of immigrants, some naturalized already, some not there yet but trying. You'll find only few places so open to migrants in this world, we are doing our part of sharing, continuously. But this is not the way world can be fixed in long term.
What is of of main issues now (at least to me & people around me) is (potential) pace of immigration and its potential to grow exponentially - we don't have endless space to absorb as many economical migrants as there are/might be. Our economies are not in super good shape, unemployment is bad in many places (or outright horriblein southern parts, 50% unemployment of youth has/will have devastating effect on future shape of these economies).
If they could financially and there would be +- guarantee of success, half of Africa (say 300 million) and massive amounts of Asia would stand up and try to come here, leaving their dysfunctional home countries. And we all know that there are some really bad places to be born to. For example, many many young people from North Africa, ie Morocco are trying this either via boats or turkey/greece border for many years already.
If somebody takes few 1000s kms journey through 10 different sovereign, stable and peaceful states and decides to end up in say Germany, he is not refugee fleeing for his life - that status ends after he willingly leaves first safe country. I don't blame them, I would do the same if I had the option, but let's call things with proper names. And there are some limits for economical migrants of how much our societies can/are willing to absorb.
Another topic is a major failure of immigrants to integrate in the past and accept european values (there is plenty of exceptions, but they are what they are, exceptions). But that's a topic on its own, and highly controversial one.
I am for example economical migrant myself, albeit only within europe (Slovakia -> Switzerland). First thing I did is to accept all the rules of my new country, don't expect that world will bend for my needs and expectations, and just be part of society, learn the language, etc. I am still amazed how Swiss are tolerant when their tiny country is overrun by foreigners.