Why do turntables sound different?

So far scientists among us don’t participate, and I suspect I know why - they have no idea.
If all seemingly great turntables sound different, than perhaps none of them sounds quite right. Each distorts and colors the sound in its own way.
I would also assume that mechanically matching table and arm could be important. And cartridge is the third element. Maybe all three should be matched ?

"Maybe all three should be matched"

I would add everything thing else in the chain.  One size fits all does not really fit in audio regardless of the ad copy and graphs.

Look at Michael Fremer's set-up in that small room with the Continuum TT and big Wilson speakers! I bet he's not too worried about vibrational interference, since the Continuum is a hefty beast indeed!

Actually, Mr. Fremer wisely gets quite nervous about vibrational interference. That's why he uses the super duper Minus K negative stiffness isolation stand for the Continuum. The new Obsidian version of the Continuum incorporates a lot of vibration isolation in its design, including magnetic levitation for the platter and a dedicated isolation system for the tonearm. The Continuum might be a hefty beast but the Earth is a heftier beast. 

'Taking care' of vibration will have some effect on resolution, which may or may not make the turntable sound better. Given the limitations of analog playback, it's highly subjective and system-dependent.