In our area, it used to be customary to have the Seller pay for a termite inspection of the property. Recently our standard contract changed to where it doesn’t mention this report, so the Buyer either pays it, or has to amend to their offer asking the Seller to pay for it. This small change means that it’s almost always the Buyer who pays for all the inspections of the property. Buyers often ask why the Sellers aren’t paying for these inspections to show that their house is in good shape.
First and, perhaps, most important, there is the importance of bringing in a neutral third-party. You don't pay the used car dealer to inspect the car he is selling you. So you don't want the home inspection controlled by the Seller. This isn't really a question of whether you can trust the people from whom you're buying the house. It's a matter of having the inspectors working for and reporting to you, not to the Sellers.
Secondly, it is up to the Buyer to determine how in-depth they want the inspections to go. Some Buyers are OK with a general home inspection that will give them an overview of the home. Others would like separate roof, chimney, HVAC and drainage inspections in addition to the general home inspection. This is especially true for those Buyers that had trouble with their last home purchase because they didn’t do enough inspections.
If we left it up to the Sellers, they’d probably opt for the least amount of inspections as possible. Most Sellers honestly just aren’t aware of the exact condition of each component of their home. My favorite line is when a Seller says, “Why do they need a roof inspection? This roof is over 30 years old and it hasn’t leaked yet!”