The appointment of Supreme Court justices by the executive branch with confirmation by the legislative branch is part of the checks and balances designed to secure separation of powers. Moreover, the Framers recognized that an independent judiciary is necessary to safeguard constitutional rights, which would be opposed by the political majority.

The system is not the "behind closed doors," secretive process you imply. The decision is the result of federal litigation with testimony, a district court ruling and published opinion, followed by a Notice of Appeal that identifies basis for appeal, briefs submitted to the Circuit Court, an appellate decision, citing precedent, fact and Constitutional provisions, a petition to allow an appeal to SCOTUS with briefs a decision granting allowance of appeal, oral argument of the parties before the Court and a final published and read decision with dissent, all of which are done in the public. It doesn't get any more open than that.

If you want an elected Supreme Court, you deal with justiceswho receive large sums of money from nonprofits, who don't disclose their donors, and PACs.

As far as the 5-4 decision, keep in mind that the Heller case, which in 2008 found an individual right to own a firearm under the Second Amendment for the first time in American history, was a 5-4 decision. It's disengenuous to condemn the process only when it yields results, with which you don't agree.

And keep in mind that the DOMA decision is limited in scope. The federal government must recognize the valid marriages of its states. It does not make a broad, sweeping proclamation making gay marriage the law of the land.