Probable cause does not apply because criminal conduct is not alleged for justification of the search.
I agree that criminal conduct is not alleged as justification of the search. But whenever that is the case, the search is
ipso facto unreasonable. The very purpose of the Fourth Amendment is to prevent the government from searching private property, except when there is an actual, reasonable expectation of discovering incriminating evidence.
As I noted, however, the government may condition the grant of a discretionary benefit on the surrender of constitutional right, but only when that right is related to the benefit. The right to be free from unreasonable searches is entirely unrelated to receiving welfare benefits. But when a defense contractor is building jets, and the government wishes to inspect those jets, there is an obvious nexus.