Theoretically, but that is not the reality I think. Imagine having such a speaker but it was turned off on the day you have no alibi. Suspicious?

Certainly not enough to convict someone, but there could be other unfortunate factors.

If you ask for a lawyer immediately and don't say anything else, then police must prove your guilt.

However, if you allow questioning to proceed, you cannot always stop the questioning in the middle with the same rights as above.

Also, in the US, improperly obtained evidence is seldom thrown out of court for some reason. Arguing that a warrant wasn't obtained doesn't always work.