As an atheist, this soul topic is rather pointless to me but I understand the poetic attraction of it. A turntable or any hardware is just a product, a thing, made by people and its design and mechanism reflect the mind of its maker. But very often, I believe, the designers themselves are clueless. Sometimes, it's just a happy accident. Sometimes not. I think most sonic traits or inherent qualities are quantifiable if we look close enough...
To me, the degree of "soul" or soulfulness in a turntable depends on the motor and the compliance of the interface, be it a belt, an idler wheel, or magnetic force. So the degree of three major components, Torque, Compliance, and Cogging play into the overall sound or tonal character of a turntable. Hypothetically, if we have several turntables using the same material and parts, how a designer dial up or down these three things will determine the majority of the sound in each table. Material, mass, isolation, vibration control, machining tolerance, execution, etc... fill up the rest of the recipe.
I think the motor is the heart of a turntable. Your mileage or soul-meter may vary.
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