That's precisely the contradiction. For instance, a house satisfied a social need or want (to keep someone protected from the elements), which is what gives it value to begin with, after all, nothing can have value without first being an object of demand. But strangely, people buy houses to "use" their exchange value, i.e as an asset. Most houses were never designed to be imbued with the sort of labour which makes them valuable as assets, but rather the sort of labour which makes them useful as actual usable homes. In fact, the focus on exchange value means that houses will deteriorate while people collect rent.
Exchange value appears as use-value, but that doesn't make it essentially use-value; while marginalism would say that I sell a product because I "value" (verb) the money more than the product, Marx says that when an object is to be exchanged, I see no use-value in it at all. But of course it has social use-value, because it can fulfill wants and needs.
"The form of use-value is the form of the commodity’s body itself, iron, linen, etc., its tangible, sensible form of existence. This is the natural form (Naturalform) of the commodity. As opposed to this the value-form (Wertform) of the commodity is its social form."
The question Marx wanted to answer was why the actual concrete form of the product appears in the relation to others (for instance, you can't say "20 yards of linen are worth 20 yards of linen", you must say they it is worth "1 coat" or "20 cwt. iron" etc.). The contradiction is that qualitatively different things can be quantitatively the same in value, but this quantitative measurement necessitates a differentiation in quality.
>Thus through the relative value-expression the value of the commodity acquires, first, a form different from its own use-value. The use-form of this commodity is, e.g. linen. But it possesses its value-form in its relation of equality with the coat. Through this relation of equality the body of another commodity, sensibly different from it, becomes the mirror of its own existence as value (Wertsein), of its own character as value (Wertgestalt). In this way it gains an independent and separate value-form, different from its natural form. But second, as a value of definite magnitude, it is quantitatively measured by the quantitatively definite relation or the proportion in which it is equated to the body of the other commodity.
>Is there a Marxism that doesn't depend on the dialectic? Or just on the dialectical mode of presentation?
Yes, John Elster, G.A. Cohen, Roberto Veneziani, Andrew Kliman, Anwar Shaikh, Nobuo Okishio, David Laibman, Naoki Yoshihara and other "analytical Marxists" have at least attempted to either explain Marx and capitalism without such dialectical concepts as value, for instance the theory of hitsorical materialism, or they have attempted to concentrate on the purely quantitative theory of value which can be neatly expressed in neoclassical economic terms (game theory and matrix algebra) to the end of various competing theories which are readable to economists rather than philosophers. The success to which they excise the "mysterious" parts of Marx is up for debate, and I think that a lot is lost in analytical formulations thus far - but the attempts are admirable and perhaps fertile for further research.
I agree with what you're saying on simplicity, but Marx's writings are deep and many-layered and open to several interpretations and re-formulations, to the point where it's hard to speak of him without advancing your favourite interpretation.