I've written about this before. The right to silence is more properly thought of as a requirement on the part of the police to find evidence and make their case without the accused assistance. The police cannot legally compel you to incriminate yourself... with the corrollery that you cannot be legally compelled to exonerate yourself either.
This means that it is just a logical result of normal "assumption of innocence".
There has been a lot of discussion of this in relation to corruption and child abuse. eg. in the Herald. Police complain that their investigations would go much more smoothly but for the silence of witnesses. Well yes, I imagine their job would be easier if people would just confess the second they saw a blue hat. It would be easier if we all stayed home, sat around the dining table, with our hands out in front of us. I don't see any of that happening any time soon.
The implication is that witnesses are trying to protect the accused. But we should bear in mind that these witnesses are being expected to relate events to which they may be accomplice. Especially under new laws - witnessing child abuse and doing nothing will be a crime, and so you have even more incentive to remain silent.
Did the police offer immunity from prosecution? This would satisfy the normal interpretation of the right as the "privilege against self-incrimination" outlined above. One suspects not.
Where you have lots of suspected witnesses, you can interview them separately and offer immunity to the one who first spills the beans... setting up a prisoner's dilemma.
The right to silence is one of the older legal rights on the books, predating the Heralds misleading mafia references. True, it was established in a time when most people were much less educated than today. However, regular folk are as unfamiliar with authority, police powers, the law, and so on, as their Elizabethan counterparts. Most people cannot afford a lawyer and talk unwisely to the police.
The protection is still needed.