It only seems weird if you think of Miranda (and various other procedural protections) as a "gotcha" to hinder police efforts, instead of what it is: a way to keep people ignorant of their 5th amendment rights from incriminating themselves. That's the alpha and the omega of Miranda. It's not a search and seizure protection at all, which is why evidence obtained as a result of a Miranda-less interrogation is nonetheless admissible.
Unfortunately, too many people conceive of the 4th and 5th amendment protections entirely as roadblocks to hinder police for the sake of hindering the police, instead of the targeted checks on police behavior that they are. In doing so they read important parts of the amendments (e.g. "unreasonable" or precisely what a protection applies to, or precisely what sorts of activity a protection prohibits) completely out of the text of the Constitution.
Unfortunately, too many people conceive of the 4th and 5th amendment protections entirely as roadblocks to hinder police for the sake of hindering the police, instead of the targeted checks on police behavior that they are. In doing so they read important parts of the amendments (e.g. "unreasonable" or precisely what a protection applies to, or precisely what sorts of activity a protection prohibits) completely out of the text of the Constitution.