SIMBAD TAP queries seem to indicate there are no distance measurements for a great many nearby stars, including Alpha Centauri or Barnard's Star
Well - not sure why distance and parallax tables are empty, but I missed something super simple, the PLX_VALUE column on the BASIC table.
SELECT * FROM BASIC  WHERE plx_value IS NOT NULL ORDER BY plx_value DESC
OR convert to distance with D = 1000/PLX_VALUE for dist in parsecs