Wow you really don't understand immigration laws. Let me make this simple and clear:

Countries do give visas for immigrants... a fixed number of them. I don't know of any first world country that hands out unlimited visas. You also have to have skills to apply for a visa; the whole point of visas is you are bringing people to your country that will make your country stronger, letting in someone who is a subsistence farmer in subsahara Africa will not strengthen your country enough to win out over a talented programmer from the same country. Then there is the time constraint, visas can take years.

So if you are not one of the people who got to apply, or were rejected because you didn't have a skill that the host country wants, or you didn't want to wait another 3 years before going, then your only choice is to sneak into the country. That is what these people are doing. They are not all asylum seekers, they are economic immigrants. Sure they will claim asylum if discovered, but that is only to invoke international protections that prevent immediate deportation.

These people are economic migrants that bring much of what they are trying to escape to the Western World. They do not have the objective of properly immigrating and integrating, and they are not true asylum seekers. The best thing Europe can do is realize that this is no longer working, and start sending the ships back around.