Can the concept of personal singularity as a philosophical vantage point ever be defended?
In attempting to redress what it sees as a central error in the Western tradition, Existentialism makes another: the indefensible (or at least undefended) positioning/prioritising of the Self as a fixed (ie: privileged, without license) point in existence/being.
Just as there are no true fixed points, or centrality, in physics - merely 'useful' contingent vantage points relevant to specific enquiry, so our conception of ourselves as discrete individuals is merely a sense impression.
It could be correct, but it is no basis from which to start philosophising, or on which to build a system (even an anti-system).
To say "I am going to die" - a great Existentialist profundity - is really a kind of anthropomorphism of the natural process it references.
All discussion that treats the Self as a discrete unit is an anthropomorphism of the cosmic perspective.
The later Heidegger was on to this, and spotted it as a failing in Being And Time, but he did not see that the same arguments apply to Time as to Being.
With neither defensible, without demonstration, as facts in the world, Existentialism falters.