You are confused. You can decline to have your papers searched by declining to participate in the activity. Therefore, no matter how unfair, it is not forcible. If the government passed a law forbidding the sale of water to people who did not consent to a search, that would also be lawful. The Constitution does not forbid bad laws.

The law isn’t so cut and dry like that. The court would absolutely rule that since water is an unavoidable necessity that this constitutes an unreasonable search. But I agree that if challenged they would be fine with a search when applying for a mortgage.

Yes, there would be a gradient somewhere. If that law extended to the point where you couldn't get utility water without a background check, some judge would find cause to throw it out mainly because of how silly it was. But on the other hand the water content of even a mildly alcoholic beverage doesn't make showing ID an unreasonable search. There are lots of ways the government can twist your arm into a "search" through this opt-in approach.

> would be lawful

yeah ok until a court challenge occurs

Good luck with your court case concerning whether or not the government can require your real details to be on your driver's license.