You know, I would agree with this idea IF once you respond with a denial or an assertion you did not do the crime and were yet prosecuted, unsucessfully for it, you could sue, personally, all the people in the prosecution team who did not listen to your protestations of innocense.
And suppose you are a confused elderly man/woman suffering from dementia, remembering from your youth that you have a right to be silent, and so you take it so as not to be confused. The police observe your condition and take advantage of your confusion and dismay at being taken in for questioning to talk you into a confession.
Let’s not give them an inch-—they’ll take a mile.
The problem the British version forestalls is concocting an alibi in connivance with friends and relatives. If the cops ask you where you were last night, and in fact you were burglaring Mrs. Sweeney’s home, and you say, “playing pinochle with my cousin”, the cops can interrogate your cousin before the two of you confer to concoct an alibi. If you clam up when initially interviewed, and later rely on the pinochle alibi, a jury is entitled, in the British system, to doubt the veracity of the alibi.
Law enforcement officials have broad immunity from liability for unsuccessful prosecution for obvious reasons. The immunity does not apply to malicious prosecutions, where they know the defendant to be innocent. As a practical matter, protestations of innocence by the accused have very little probative value.