A lot of this is new to me, even after buying a couple of homes, known people who inspected homes for banks, buyers, and government.
They all have different purposes with only some beneficial overlap.
An insurance company is looking for the common risks that they have to pay out for, pointy stuff the neighbors will trip and impale themselves on, how much it might cost to replace something, and a general sense of their customers behavior and risk. They are not expected to find, nor are they looking for, any non obvious construction or maintenance defects.
A bank's main focus is on the value of the land and structure, i.e. square footage and whether it is being reasonably maintained so it can be repossessed and sold. Both banks and insurance companies can and will stop by and visually inspect your property whenever they feel the need and will share this info.
A home inspection at the time of sale is to educate the buyer on what exactly they are paying for and what they may need to improve in the future, etc. Most of these details are private, meant to help make a decision, not to help your insurance company deny a claim. It would be foolish to freely hand this over unless obligated.