incorrect and overly worded addresses

The response to a search is not the address stored in OpenStreetMap. It is a structured set of address elements which can be associated with the object queried. You can see how this structure is worked out here (https://nominatim.openstreetmap.org/details.php?osmtype=N&osmid=500367365&class=amenity) on the dedicated website of Nominatim, the relevant search engine. Nominatim tries to provide information which may be relevant across the globe, therefore not every element may be necessary for forming a valid address. More usually applications call the Nominatim API and select the elements of the address which are appropriate to their needs: in Britain this would usually be house number or name, street name, settlement name and postcode. Elsewhere different elements may be needed.

In general dont get too worried about how something is presented to you from the OSM website: these are usually best regarded as examples of what can be done rather than definitive ways to use the data for particular purposes. It's certainly a bad idea to manipulate the data to achieve a particular outcome with one tool because doing so almost certainly breaks a lot of other tools. See "Tagging for the Renderer" on the wiki.