Yes, it sounds reasonable. It also sounds reasonable to allow police to enter anyone's home at any time - consider all the crime they might prevent if only they didn't have to wait for a warrant! It sounds reasonable to let the police shoot a fleeing suspect, because why are they running if they aren't guilty? It sounds reasonable to let the police look through any computer - how much CP is missed because they have to wait for a warrant?

Lots of things sound reasonable which are not. One must consider the downside, particularly the downside of abuse of power.