You've got this part exactly right.
That implies directly and logically that REASONABLE searches are permissible.
And here, you are so close to having it right. You just didn't take it far enough.
Unreasonable searches cannot be done under any circumstances. Reasonable ones require a warrant AND a basis for the search. It's not a fishing expedition.
"... and no warrant shall issue but upon on probable cause, supported by oath or affirmation, ..."
There will always be those who argue the 'necessity' do to more than is allowed. But these searches are a relatively new thing. One thing or another has always caused concern for safety, but only recently -- in our lifetimes -- have we succumbed to the siren call of safety over liberty.
HOWEVER, a warrant is NOT required for all reasonable searches.
There is no language that says directly or even implies that a warrant is required.
It simply states thatno warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
Again, there is NOTHING that says there has to be a warrant for a reasonable search.
If you still disagree, please provide the quote for me.
Do Customs agents need warrants to search luggage? (Yes, I know, there is a facade of consent, but that consent is coerced.)
Do arresting police officers need warrants to search suspects or those being arrested? (No consent by the arrested party requried. No warrant, either.)
No, since those are 'reasonable' searches.
I believe that the Founders did not want to see random personal or home searches just for fishing purposes. Those are unreasonable.
But when there is 'reasonable' suspicion of wrongdoing on the spot, warrants were not and are not absolutely required.
When a warrant is requested, it has certain criteria that must be met.
I think we need to stick with what the Constitution says, not what we wish it says.