How else could you look up your unclaimed property without this information? I don't see a better alternative.
I would (naively) assume that if the government is confident that your address is correct and up to date, they would inform you of said property à la USPS instead of posting it online for all to see.
It should not provide information that the user did not enter. If you didn't enter your address it should not spit one back to you.
(Also, address is not a good way to identify most millenials, who move every 1-2 years. E-mail is a much, much more stable identifier than a sleeping location.)
There used to be a thing called the phone book that would tell you where people sleep as well.