What's to prevent me from classing a warrantless search as unreasonable?
Such a stance actually seems very reasonable as a warrant is to delineate the scope, purpose and target of the search; a search without these bounds is unconstrained and therefore I would consider it unreasonable.
You can consider anything you want. (As can I, and any other citizen.)
The courts have from the earliest days of the Republic defined what searches are unreasonable. Your opinion or mine is perhaps interesting, but neither of us is designated by the Constitution to settle points of its interpretation.
The Constitution says “unreasonable” searches are prohibited. Determining the boundary between “reasonable” and “unreasonable” searches is exactly the type of thing the Founders intended the Courts to do.
The Founders could very easily have just deleted the first clause of 4a, and just prohibited any and all searches without a warrant. They chose to include the “unreasonable” language for a reason.