I would wager a guess that many people have dropped place points named "Home" and not setting them as private. Inexperienced editors may have approved them and, as you have discovered, they are completely searchable by anyone.
You can set them to residential/private through the map editor.

Are you willing to share the general area where you yielded a high number of *apparent* private residential search results? I ask so that we can search around that area to find bad place points that were saved as "Home" so we can convert them to residential place points (RPP's). You don't need to share a private address. Just a general area, such as a major intersection and city name, or if you are uncomfortable with that, a city name (and state) by itself will still be useful.

You should also note that instead of adding a place called home in Waze, you can just set your home (and work) location on the main search menu. Those two locations will always appear at the top of the list, with your most recent navigated locations below that.

Another Southwest editor here...
As editor come across these places title Home, Casa, etc, we change them to residential place points that don't include the name. We will also review the photos to make sure they are appropriate.

You can even do some of this. If you search for Home as you said, you can select the place (but don't navigate to it) and tap the three dots on the information page. From there you should be able to choose to edit the place. On the edit screen, tap the non-obvious button that says "This is a residential place" (or whatever it says - going from memory).

That will be put on the map for review and one of us will get to it.

However, for your case, I suggest following what SunDevil2213 says - make it your home setting and use the Home option that's at the top of the list when you first hit the search button.