An inspector checks the systems a walkthrough cannot: furnace age and function, roof condition from the attic side, foundation moisture, and electrical panel capacity. None of that changes based on how the purchase is financed, and a seller accepting a cash offer is not asking you to skip it.
If you want to compete on speed without giving up the inspection entirely, shorten the condition period rather than removing it, and have the inspector available to move quickly once your offer is accepted.
Speed and diligence are not actually in conflict if you plan for both. Get your hand-reviewed valuation from Joel Dyck.