Rate these on order of importance:

Unsound...No they don't.

1...The signal.
a. The disc or LP being played. (The ultimate limit on quality).
b. The playback equipment, disc player or turntable and pickup. (How well the disc's potential is realized).

2...The speakers.
a. Type of speaker (planar, box, etc) , and make and model.
b. Number of speakers and their placement.
c. The room in which the speakers operate.

3...Amplification.
a. Active circuitry.
b. Speaker wires (Importance depends on length required).
c. Interconnects (Importance depends on active circuitry details).

As a special case for LP's only, turntable mounting provisions may rank somewhere at the top of the list if you have a problem with vibration.

Unsound...Since when do audiophiles agree on anything?

I think that the order of importance changes as you go up the price scale.

For a system below $1200, the speakers will be the limiting factor. (Disc player, $250, Amp,$400 Magnepan MMG, $550). Going up in cost, I would still put money into better speakers up to about $2000 in the speakers alone, at which point improved source, Disc player/phono pickup would probably get more results than better still speakers. Around $3500, the low cost (but decent) amplification would begin to be the long pole in the tent. When you get to $6000 or so, personal preferences begin to dominate, and what's most important for one person isn't for another. Room design and treatment may offer dramatic improvement, but is not an option until you are way up on the cost scale. (Lots of "Bang" but lots of "Bucks" too).