That's just an excuse. Germany and UK have much higher populations and manage to achieve similar results. The "more homogeneous" argument is weird to me. Most immigrants that I've dealt with are more inline with the European mentality (regardless of their country of origin) than US natives. Are you saying the problem is with the locals?
A valid question and one that is getting much less attention than it deserves (probably because some of the answers are rather uncomfortable).
Locally, welfare can be egoistically motivated. Just about everybody would be willing to pay serious taxes to raise that one beggar off his doorstep - if only to keep him out of sight. We like to think of that as altruism, but it hardly is. Now ask those same people to pay serious taxes for the benefit of poor people thousands of miles away and you get a completely different picture.
Enter mobility: If you raise "your" beggar, someone else might just hope that theirs will go to a place where they will be raised (your doorstep). Clearly, egoism won't work as a motivator anymore because you don't want to be the new charity central. Therefore, welfare has to happen on the same organizational level as freedom of movement and that's where the relative unwillingness to help those thousands of miles away comes in again. Even basic income suggestions quickly lose their pie in the sky utopia feel when it comes to the question of access/citizenship/migration.
The US was literally built on mobility as a substitute of welfare, but once the original anti-welfare "stay poor or go west" was exhausted, the inherent antagonism between mobility and welfare continued to stay obscured behind other ideological concepts, "temporarily embarrassed millionaires" and all that. The EU is learning the hard way, but it is impossible to separate valid concerns and solution-finding from all the noise of and about stupid racism.
As technologists, we also know that getting popular is one of the worst things that can happen to a community. Scaling community and relationships is super hard.