Well I don't think "anyone" in Europe wants to send these migrants to the bottom of the sea. A solution currently worked on is to pay other countries closer culturally, socially and even geographically (i.e Turkey) to host these people.
The lack of border security gives a sense of unease especially if you expect people from a war torn country or a country where crime is high so I fully support securing the borders.
However the deshumanisation of migrants and treating them as criminals (or worse) is totally wrong and has no place in a civilised country. You can have both border security and immigration. Just be honest who is allowed in and who is not, put in place agreed quotas and that's it. At least everyone knows(including the migrants) what your stance is.