What is most important part of a system?

There is an expression that someone who represents himself in a courtroom has a fool for a client. Now, I don’t want to be too alarmist here, but I believe that expression can also be applied to the listening room. 😀 And I’ll go out on a limb and speculate that the reason why many audiophiles are always in upgrade mode and can’t get no satisfaction is because, drum roll, if you don’t learn from the mistakes of the past you’ll just keep on making the same mistakes. How can you explain why some audiophiles have had, let's say, twenty systems or fifty systems?

My audiophile answer is the loudspeaker/room interface, but my real answer is my wife and family.  Without them how much would I really care about how my system sounds?  Call me sentimental.

OP, your final analysis has a complete dependency on what turntable and what CDP was used to arrive at that conclusion. Different models of each would have resulted in a different conclusion. All things being constant including the listening room, listening volume, and the music content, I personally think changing the speakers will make the most sonic difference in a system.

This is how I would put in order:
1-Source
2-Room
3-Speakers
4-Amp
5-Pre-amp
6-Power
7-Cables

I can sort of agree with this order, as long as the recording is considered as part of the source. i.e. Personally, I find the recording quality to be at least as important as the source quality.

1) Source/Recording
2) Room/Speaker interface

And I’ll go out on a limb and speculate that the reason why many audiophiles are always in upgrade mode and can’t get no satisfaction is because, drum roll, if you don’t learn from the mistakes of the past you’ll just keep on making the same mistakes. How can you explain why some audiophiles have had, let's say, twenty systems or fifty systems?

As one who has done a lot of experimenting with gear through the decades, I can own up to this.
Again, for me, the problem falls back on the recordings. Some recordings just sound better with different equipment. I think I would probably change gear less often if I had more systems. Then I could tune them to suit my tastes to different styles of recordings.

Have a system for bright recordings, a system for warm recordings, a system for 80's digitized recordings, a system for high resolution quality recordings, etc.

I was at a fellow audiophiles home about 10 years ago who had systems setup like this. A SET/horn system, dynamic/SS system, dynamic/tube system. His main system even had one turntable with 4 different arms/cartridges/phono stages. He used a different arm/cart/phono stage for different types of recordings.

Unfortunately, I am forced to try to find one system to do it all. 
While a multi-arm turntable is not out of the realm of possibility, I'm not there yet.
As time moves on, and the recordings in high rotation change, so does my opinion of my systems sound. It's like trying to hit a constantly moving target.
I suppose I could just listen to the same 50 recordings over and over again, the ones that make my current system sound it's best........nah.

@onhwy61 that's not sentimental, that's keeping it real. Perspective is your friend, thanks for the reminder