That is a gross oversimplification of the issue with ahistorical conclusions. In fact, there were plans made at various times throughout the war to appoint such a judiciary, including some supported by the administration. The states rights faction in the CSA Senate blocked it though, not to give Davis unchecked power but rather because they feared that a judiciary appointed by him would be used to infringe upon the authority of the states themselves. In short, they feared judicial activism that would transfer power from the states to Richmond, so the move was actually to RESTRAIN the power of the national government!
The confederate constitution did not mince words. The judicial power of the confederacy was to be vested in one supreme court and such other courts as the congress would establish. It's right there in black and white. So what you're saying is that Davis and the congress deliberately ignore the constitution by refusing to establish the one institution which could keep them from ignoring the constitution? Neat trick. And you complain about Lincoln.