The short answer is that dead space is small in absolute terms and huge as a fraction of a small dose, which is why it feels like a rounding error and behaves like a systematic loss.
The luer cone of the syringe plus the needle's own plastic hub accounts for the vast majority of the dead space.
The relevant detail is that the needle lumen volume is under a microlitre in a typical fine-gauge configuration, so the needle is not the problem.
One qualification: the dead space does not affect the dose accuracy if the hub was full of solution at the start of the draw.
The switch nearly doubles your vial, which is better than most other optimisations combined.
edited 8 Dec 2024 by ines_brandt — removed a claim I could not source