How can the American legal system justify itself morally if it jeopardizes, through its own rules, the right of law-abiding citizens to personal peace and security?
In my mind, there seems to be a couple of issues in the question that need to be defined and clarified. The first issue is the "moral" question regarding the legal system. I tend to think that the American legal system roots itself more in what can be negotiated and what can be understood as practical and legal reality, as opposed to being negotiated on a moral basis. The legalism of the American system is one in which moral objectives are placed in an evidential sphere. Morals are something that the legal system in America tries to avoid. Terms like "not guilty" are the replacement for "innocent," a term that involves more of a moral standing than "not guilty."
The second issue is the jeopardy being suggested. More detail is needed here. I think that a specific example is needed to substantiate the claim of a tradeoff as being evident. I think that the American legal system starts with a premise in which individual rights are used as a type of shield against encroachment from an external force. This sphere of individual entitlement is the line, the frontier, that the external force cannot cross. I think that more specific information is needed regarding where this exact jeopardy lies. Some might argue that the recent debate on guns in America is where there is a jeopardizing of "personal peace and security" in terms of seeking to enact meaningful gun reform. I think that specific information would be needed as to this point. However, in my mind, there is nothing to suggest that the Second Amendment be abolished or repealed. No one is debating the reality of gun ownership. In this, there is little risk to the amendment, which guarantees individuals to own firearms. Gun control and legislation to support it does not automatically mean a repudiation of the Second Amendment. It is here where the negotiation of the American legal system is on display. Legislation can be debated and discussed without removing the amendment, something that would not be possible if a moral imposition is featured, making negotiation that much more difficult.