It still is profound whatever one's definition of same. Pick a definition of same. Make it as precise as you want. It might be totally compatible with some of those definitions you come up with. For all others, The Ship Of Theseus still makes a powerful questioning tool that raises insights to question those "single, precise" definitions.
There's a naive (mostly anglosaxon/empiricist) idea that philosophy is just noise because of the conflicting definitions of things.
Whereas it's the total opposite: questioning and disecting the definitions we use (and what they presuppose), is the exact role of philosophy.
The Ship of Theseus (and countless others ideas and paradoxes) are tools in questioning those beliefs and "definitions".
Those examples don't stem because of our confusion about what is same -- they are tools to probe what we consider same, to poke holes in our idea of sameness.
And I call the objection to this naive, because having a "single objective definition" is not something possible (like science doesn't claim to know some ultimate "reality", just to make ever better models and approximations of it).
We have to live with various ideas about identity/sameness, and we need philosophy and arguments like The Ship, to question them and see their partial nature.
