In reality the way it would work is the prosecutor and police would use every bit of circumstantial evidence to construct a claim of motive, means, and opportunity. Then threaten you with a lengthy prison sentence if you are convicted.

You're not going to roll on whoever really did it (assuming you know), and trust your fate to a jury understanding presumption of innocence, and being convinced of "reasonable" doubt, without you saying a word in your own defense? Most people would not unless they had an iron-clad alibi, but if they did, they wouldn't be getting charged in the first place.

There's a big difference in when you break silence though. Strategically, much better to keep it until all the facts are known to your side. At the start, the police/government have the informational advantage. In other countries, even delaying (but eventually speaking) can allow a negative inference to be drawn. The right to silence is important even if you eventually speak.