Switching pre regulator and linear regulators
No, this sounds reasonable, if it is what you want to do. One problem is that you will drop 9-6=3 volt at 4 amperes, that's 12 watts. You need a hefty heat sink for that.

A better option is perhaps to have a 6V output from a switching regulator, and a 5V low-dropout linear regulator, converting 6V to 5V. The 5 volt regulator would only have to drop one volt, converting 1 watt into heat. This is still a non-trivial amount of heat for one IC, but as peufeu mentions in a comment, is small enough to be dealt with using the copper on the PCB as a heat sink.