What if there’s something illegal, violating copyright, etc. on the site? Or to take a less legal example, what if someone’s site is hacked? You need some way of getting in touch with the owners.
The snail-mail address of the registered agent would suffice. The cost of postage is sufficient to deter the least-determined spammers. And the most-determined spammers would be deterred by the most potentially profitable targets having legal departments handling the mail received by their registered agents.
Atleast in my area websites are also required to carry legal contact information somewhere on the site, which is far easier to secure against spammers than the WHOIS database.