Scott pointed out half the problem, same as me
If you're asking the court to do the research, you're creating a huge change in the way courts operate.
Now you seem to be saying it should be the recorder to makes the determination. Box already said, and I gave more detail, that the recorder doesn't do research either. They just record everything. It's been this way for decades. (If not centuries.)
You say, "someone who their documents show as NOT owning the house," as though there is a document for every property, continually up-to-date, with a single field on it for "owner". That doesn't exist.
The recorder keeps a stream of documents, which can be searched for and collected, which relate to (or may relate to) a property. Someone receiving this collection of documents can review them in chronological order to determine any apparent interests in a property.
If you've only ever bought and sold houses that had clean title (see my other post) then it might have appeared easy when you saw the paperwork at your closing. "Yes, that document there says the title was transferred to the previous owner in January of 2001."
As soon as you start dealing with liens, second mortgages (to different lenders), past-due taxes, lawsuits from contractors, and of course foreclosures, that pile of papers can get really big really fast. And many of them are claims against the property, which may or may not be legitimate.
It's not simple, just because you want it to be.
