Tthough lack of a requirement for legal immigrant status and a likewise lack of remuneration may enable fake asylum claims, to go in the other direction and require legal status and money would stand to hurt the honest asylum and refugee applicants whose very lives may be saved by the protection of the federal government. It would not make sense to punish everyone for the sins of a few bad apples. Also, those who call for the immediate expulsion of all failed asylum immigration attempts would be wise to consider that for which they wish.
These individuals are likely not giving credence to the argument that deportation is not a cheap exercise. Thousands of dollars are potentially spent per failed asylum applicant, not only to oust them from the country but also to provide them basic rights and resources prior to their deportation. So, while there are some noticeable flaws to the asylum immigration system, the cure may be worse than the problems. Enforcing the law is important, but not if it hurts the constituents it is designed to protect in the long run.