In classical predicate logics, why is it usually assumed that at least one object exists? In classical predicate logic it is commonly assumed that the domain of objects is non-empty. This validates inferences such as $$\forall x Fx \models \exists x Fx$$ as well as, if the identity predicate is available, the logical truth of $$\exists x~x=x.$$ What is the motivation for this assumption? In reality it is arguably not a logical contradiction to assume that nothing exists.

If you allow the domain to be non-empty, then you need to introduce more complexity to handle non-logical symbols.

You can relax or eliminate the assumption of domain non-emptiness, which gives you various flavors of free logic.
Free logic on the face of it addresses a slightly different problem, namely how to handle constant symbols that happen not to refer to anything or partial functions.
However, these are questions that you need to address if you want to allow constant symbols in your non-logical vocabulary. In the theory of Peano Arithmetic, for example, there's a constant $0$. In an empty structure, there's nothing that $0$ can refer to ... so it's not clear how to build a structure with an empty domain that could be or not-be a model of PA.
