I'm deeply concerned about your view of humans. This kind of misanthropy has been used to justify the death of millions throughout all the past century.
You're not even consistent. First you portray refugees as lazy welfare hogs, now you say they are wealthy because they can afford the smuggling gangs. If they are so wealthy, what makes you think they only want to come to Europe to collect unemployment benefits?
Someone applying for asylum in Germany can be stuck in limbo for years before being rejected and deported. This happens fairly frequently. Throughout that waiting period they're not allowed to work and are stuck in refugee camps that are getting less and less hospitable as the number of refugees grows (simply because the communal governments asked to take care of them don't have any money and often only learn how many they have to accommodate when the buses arrive). Refugees don't have an easy time.
If you think all of the "Muslim world" is one big cozy community you haven't been paying attention. The "Muslim world" is about as united as Ireland during the Troubles. The civil war in Syria is fought between a totalitarian dictator and Islamic extremists. Saudi Arabia is an Islamic fundamentalist dictatorship. This is the last place you want to go if you don't agree with either side in the conflict. Yet Saudi Arabia has accepted thousands of Syrians into the country (although they don't treat them as refugees, which is what led to the claim that they don't take any Syrian refugees).
And Turkey? Tons of refugees are going to Turkey. And many of them have hopes of being able to return to their home country when the war is over. To quote Wikipedia: "As of April 2015, there are 2,138,999 estimated Syrian refugees in Turkey." -- that's an order of magnitude more than any EU country (and Turkey isn't that big of a country nor that wealthy).
Heck, many places outside of Europe have granted actual residency permits to Syrians. That means they're not even treating them as refugees but as perfectly ordinary legal immigrants -- a far cry from the temporary shelter and perpetual "Duldung" (i.e. promise not to get deported yet) they would get in Germany.
You're pretending the EU countries are the only places accepting Syrian refugees. That simply isn't true. The reasons we hear more about refugees coming to the EU than those being accepted in other places is simple:
1. Most of Europe shares a common border (Schengen), so "our borders" span more than just our own country.
2. There are a ton of countries in Europe, so each country accepting a lot of refugees adds up to a very big number.
3. We live in Europe (or in the US: you're closely related to Europe) so we pay more attention to what's going on here.
Stop listening to AfD/NPD/BNP bar-room clichés and pay attention to what's actually happening outside the Western World.
Some reading material:
http://www.cbc.ca/news/world/for-many-syrian-refugees-fleein...
http://www.irishtimes.com/opinion/lebanon-struggles-to-shelt...
https://en.wikipedia.org/wiki/Refugees_of_the_Syrian_Civil_W...