Isn't that the worry? Say a bug in your timekeeping software underreported hours worked and that lead to workers not being paid their agreed upon rate. When it goes to court you now have to prove that you didn't maliciously introduce the bug to save on employment costs, whereas if it is a third-party providing the software it's their problem. "Conflict of interest" is ultimately just another way to say "I don't want to assume the liability when things go sour". Nobody cares about conflict of interest when things go right.
Again, "conflict of interest" is what people often say when they don't know if it will affect them, but don't want to take the risk. "Regulation requires it", as illustrated in the first comment, is what people say when caselaw actually demonstrates that they would be liable.
The fun thing about language is that it is fluid and can take many forms.
No, it's not.
It's "malice is not a reasonable explanation for things going wrong". It only changes liability when it follows malice, what is much rarer than you seem to think.
It is also a way to assure people that you won't do something bad.
It cannot possibly be the case that Microsoft runs on Open Office and MacBooks.
They only started eating their own dog food when people started making fun of them in public.
I've had customers complain to my face that we tailor the products to our needs, and are surprised (and sometimes vocally disbelieve) that we don't use it, ourselves.
In certain industries, dogfooding is considered bad, and sometimes illegal.