Suppose we acquiesce for the space of this post in QuineSpeak.
Then 'Horses exist' says no more and no less than that 'Something is a horse.' And 'Harry exists' says no more and no less than that 'Something is Harry.' But the 'is' does not have the same sense in both translations. The first is the 'is' of predication while the second is the 'is' of identity. The difference is reflected in the standard notation. The propositional function in the first case is Hx. The propositional function in the second case is x = h. Immediate juxtaposition of predicate constant and free variable is the sign for predication. '=' is the sign for identity. Different signs for different concepts. Identity is irreducible to predication which is presumably why first-order predicate logic with identity is so-called.
Those heir to the Fressellian position, such as Quine and his epigoni, dare not fudge the distinction between the two senses of 'is' lately noted. That, surely, is a cardinal tenet of their brand of analysis.
So even along Quinean lines, the strict univocity of 'exist(s)' across all its uses cannot be upheld. It cannot be upheld across the divide that separates general from singular existentials.
Or have I gone wrong somewhere?