[anigbrowl]

This looks like it agrees with my point: the warrant process is the objective mechanism by which the subjective reasonable/unreasonable decision is carried out.

No, the warrant process is an objective mechanism by which the subjective decision is carried out. You have no textual grounds for saying it's the exclusive method, and there's no precedential support for it either. If we were to posit it as the only reasonable mechanism, then a police officer who observed you stuffing a dead body into the trunk of your car would be powerless to delay you absent a warrant, which is clearly a ridiculous position.

The role of the warrant is to allow the police to barge/kick in your door on the basis of available information rather than having to stake you out in hopes that you'll expose your criminal activity to them, which would allow them to conduct a regular search. It's not a prerequisite to a search and never has been AFAIK.