Well, I'd equate it more to trying to stop further broken legs by teaching people how to do things properly.
The fact is that we're obligated by international law to provide safe refuge to people who need it, and qualify. Sometimes those people come from places with laws similar to ours, and sometimes (a lot of the time) they don't. Many can be taught our ways, and some can't. If we shut the door on the many because of the actions of the few, we'd be in breach of international laws and we'd be abandoning many people to serious harm and/or death.
The same argument can be applied to many situations, not just asylum. Shall we, for instance, ban all dogs because some of them kill? Should we put a curfew on all men because some of them attack women?