There are rules about this already and they seem to be appropriate (i.e. no - it is within someone's rights to demand that a lawyer be present - seems reasonable to me - most police officers are honest and trustworthy but some aren't).
No, you don't have to talk to the police without a lawyer present.
The US Constitution addresses this; read the 5th amendment
They have the right to remain silent and are not compelled to self incriminate
No. You would be denying people one of their most basic democratic rights - the right of protection from self-incrimination.
They don't have to say anything. It's called the firth amendment.
violates the Constitution .. self-incrimination clause .. so, NO