It's convenient but it also generates a huge amount of telephone spam and fake invoices fraud attempts. So I could see the argument of keeping that information private.
I still think that it's better to have it public, but it generates some additional problems that needs to be handled.
The law is in practice fairly toothless, Companies House has typically insisted that it simply doesn't have the funding to pursue errors even though it's illegal to make false filings - despite a large volume of obviously bogus information in their system every year.
It did find the money exactly once in recent years, to prosecute one person. That one person was making a point of how toothless it is, by creating bogus data that was embarrassing to named politicians. What an excellent way to make their point for them.
There are actually three levels: A public address available to anybody who knows how to enquire, an address available to a large number of authorised users, including Credit Reference Agencies, numerous government agencies and so on, and finally a home address intended primarily for law enforcement (e.g. if the director is to be arrested it wouldn't do for police to have no idea where they live). You can set them all to be the same, but you don't have to.
The reason for the last extra grade is that in the UK there are businesses which are legal but broadly unpopular. For example, somebody is breeding animals that will be used for medical research. Historically protesters have harassed the directors of firms like that, vandalized their homes and cars, physically attacked them, or threatened their lives. Such directors are entitled to request that their home addresses be suppressed from most uses for this reason.