I don't think "missing person" is considered probable cause to search every place they're associated with. The van, yes.
But otherwise, when people are missing, and if police decide to do anything at all, they stop by various places and ask the people who live there if the person is there. If they say "no," that's not probable cause to search the house!
If. that were true, thousands of people would have their homes searched each time there was a missing person's report. And many others places (motels, businesses, etc) as well. Schools.
Being missing is not a crime. It is a human welfare issue.
All police can do is ask politely.
The Laundries hadn't lived there that long, it's even possible that Gabby's van was registered to another address. What police could have done is ask to speak to BL (which apparently they did, and the parents said he wasn't available or not there).
If it was registered to Gabby's mom's address and that's the person who reported her missing, they likely wouldn't go to that house...