"Than" works as a subordinating conjunction. In "He loves you more than I love you", "than I love you" modifies "more", which in turn modifies "loves". In the elliptical form, the missing elements (which include the modified verb) are provided by the matrix clause.
"But" works as a coordinating conjunction. In "Nobody [else] will help you, but I will help you", there is no subordinate clause. Without that relationship, I see nothing to provide an implied verb to the second clause.
The elliptical version which includes the auxiliary works. That's enough to establish that the independent clauses have parallel structure, and the rest of the clause becomes obvious. The elliptical version without an auxiliary leaves us with a subject in search of a verb. We can't assume the verb that the clause modifies simply because the clause modifies nothing.
Both "than" and "but" also work as prepositions. In that case, the object of the preposition takes an objective form.