Which is the most important part of a stereo system?

For me there is no singular most "important" component.  Rather, there are important choices in the development of a system.

In no special order, type of speaker, i.e. planar, box speaker, K-horn, etc.  The choice here will often lead to amplifier choice for a variety of well documented reasons.

Then there are source choices to be made. Are you a vinyl person, or do you stream, perhaps SACD / CDs acquired over tume.

Are you a tube enthusiast, either amplifier or pre amplifier?

Any of these choices could be the most important to you, but perhaps not me.  Thus, the fragmented nature of the discourse here.

So I will share my most important choice(s).  I am a Maggie fan and that has driven my amplifier choice as well as pre amp.  Others will have different first choices, there is mo right or wrong, just individual preference IMHO.

Your room, room, and more room impact the sound more than you know. A system is a whole, they work together, power cords impact gear more than any other cable, the wrong power cords and can make a good piece of gear sound like crap. So don’t look at if I change one piece of gear as the only thing to improve your system, start with the room your using 1st and in most cases that will cost far less than a new piece of gear. Speakers interact with the room, how does a speaker sound only as good as your room allows. I see so many speakers on Youtube that are big $$$$ ones and they are in a room that kills the sound of all their gear and money they spent, it is a waste of money in a reverb hard space. Audio is like cooking what spices do you like? To each his own, tubes or Solid State or Class D, H, all have their followers, its what you like for your ear and enjoyment, no reviewer can get your system right for you, learn from experience what you enjoy the kind of sound you like then build towards that goal. We are only 0.5% of the consumer market, so we are a rare breed. Which is why what format we like makes no impact in the big picture of electronic sales. SACD, MQA are good formats but the 99.5% of the buying public doesn’t care, that why they all slowly die out, not that they are no good but most people don’t care, they want portable so a pair of earbuds and a cell phone and they are good to go, along with digital radio streaming. Audiophiles are a hobbyist group who enjoy the art of reproduction and will sit and listen, Boomers are the market when they go the market goes with them. I know of none of all my family and their family nor their friends have as much wrapped up in their home system as the cost of my power cords. They got other priorities, like kids, education, gaming, etc.

YOU are the most important part, because if you don't like it, no matter what the accessories cost, basically you wasted your money. Those that criticize what you like are not paying for the system nor having to listen to it . . . you are; therefore, listen to opinions, salespeople and do your homework . . . and if someone is ungracious in listening to your system (not talking about constructive criticisms or sincere help), then invite them to go home and listen to what they choose.

The single most influential component for playback sound quality is universally accepted as the loudspeakers. It’s been this way for decades, perhaps even from the days of the birth of audio.

No two pairs sound the quite the same, sometimes nothing like it.

That in no way is to deny that individual mood at the time of listening is not absolutely crucial to the received perception.

We all know just how good the human imagination can be. In the right mood (and company) I can easily imagine that my Sony television set sounds better than most of the systems I have heard.

Same thing can happen with the playback system in a club or a party, but only if I’m having a really good time.

Later on it sometimes becomes a puzzle as to how I could have believed such obvious nonsense.

The mind and all it’s tricks seem to be geared towards promoting survival and seeking pleasure, and not always towards discerning any form of truth.

Just in case nobody mentioned it already which they probably didn’t - the fuse, be it ever so humble. Another one nobody probably mentioned is electrical connections of all non-audio outlets. And one more nobody mentioned  - how many CDs are in the room.