  Understanding what makes Bi$_2$Sr$_2$Ca$_1$Cu$_2$O$_x$ (Bi-2212) the only
high critical current density ($J_c$), high temperature superconductor (HTS)
capable of being made as a round wire (RW) is important intellectually because
high $J_c$ RW Bi-2212 breaks the paradigm that forces biaxially textured REBCO
and uniaxially textured (Bi,Pb)$_2$Sr$_2$Ca$_2$Cu$_3$O$_x$ (Bi-2223) into tape
geometries that reproduce the strong anisotropy of the native crystal structure
and force expensive fabrication routes to ensure the best possible texture with
minimum density of high angle grain boundaries. The biaxial growth texture of
Bi-2212 developed during a partial melt heat treatment should favor high $J_c$,
even though its $\sim$15$^{\circ}$ full width at half maximum (FWHM)
grain-to-grain misorientation is well beyond the commonly accepted
strong-coupling range. Its ability to be strongly overdoped should be valuable
too, since underdoped cuprate grain boundaries are widely believed to be weakly
linked. Accordingly, we here study property changes after oxygen underdoping
the optimized, overdoped wire. While $J_c$ and vortex pinning diminish
significantly in underdoped wires, we were not able to develop the prominent
weak-link signature (a hysteretic $J_c$(H) characteristic) evident in even the
very best Bi-2223 tapes with a $\sim$ 15$^{\circ}$ FWHM uniaxial texture. We
attribute the high $J_c$ and lack of weak link signature in our Bi-2212 round
wires to the high-aspect ratio, large-grain, basal-plane-faced grain morphology
produced by partial-melt processing of Bi-2212 which enables $c$-axis
Brick-Wall current flow when $ab$-plane transport is blocked. We conclude that
the presently optimized biaxial texture of Bi-2212 intrinsically constitutes a
strongly coupled current path, regardless of its oxygen doping state.
