Therefore, one could argue that the idea of an "individual" existing through time has no objective basis to begin with, and the decision to identify entities that exist in different instants of time as the same "individual" can't be other than a subjective whim.

That's roughly my current view. Two minor points. I think "whim" may overstate the point. An instinct cooked into us by millions of years of evolution isn't what I'd call "whim". Also, "subjective" seems to presuppose the very subject whose reality is being questioned.