I've interpreted "irreplaceable" in its normal rather than literal meaning.

That's not to say I don't take care of things, or that I wouldn't be unimpressed by someone gratuitously depriving me of possessions or data.

I think the distinction I am making is that if all my possessions were destroyed by a natural disaster or accident, the fact that some of them couldn't be replaced or recovered wouldn't be registering at all in my list of priorities.