The rationale behind my ordering of importance in an audio system chain is based on what actually occurs with each part of that chain. If a task is easy, it is then easy for anyone to accomplish it. If is hard, then it takes a more proficient person to get it done. Relating that to an audio system should prompt one to examine the process of getting sound in the room for us to hear. The speakers become the component with the most difficult task to accomplish. They receive electrical energy in the form of the signal from the amp via the speaker cables. They must change this electrical energy into acoustic energy, via moving the drivers and then change it again by creating acoustical energy. The most difficult task in the process. The room actually becomes part of the speaker and as such, I ranked it second in importance, because it's effect on the acoustical energy created by the speaker will "voice" the modulated air that moves the diaphram in our ears.
The source then would be ranked next as it too much create a "change" in the signal. In the case of the CD system, digital information has to be changed to analog. In the case of a phono system, mechanical energy created by the record groove/stylus/cantilever interaction is changed to an electrical signal inside the cartridge.
The power system would be third in order of importance, because it's purpose is to remove outside influence on the signal and how it is handled inside the component it is connected to. It much pass current to the component, but it's ability to prohibit outside influences has a greater impact on what we hear.
The amplifier system would be the next in importance, because it's job is not to change anything, or keep anything from having a negative influence, but to amplify the signal for use by the speaker. Bandwidth and power headroom will make the better amps stand out.
The interconnects/speakers wire would be last in importance because their task is only to pass the signal along. Proper observation of basic electrical parameters can allow most cabling to accomplish this without having negative impact. There are noticable differences in any cable's impact on the system, but in reality it is the cable's ability to "step out of the way" when passing the signal along and not inhibit it in any way by altering the electrical properties of said signal.