A company is not a person. It cannot be found at home, and it cannot be handed a letter. The registered office solves that: it gives every company a single, publicly known location at which it can be reached formally, and at which official correspondence is directed.
That is the whole purpose, and it explains the character of the requirement. The address is not there to impress anyone. It is there so that a regulator, a court, a creditor or a counterparty always has one place to send something important and know it has gone to the right company.
It follows that the address is public. Anyone who looks the company up on the register can see it. For a founder using a home address, that is worth understanding before it is filed rather than after.