The structural complexities of the lead-free piezoelectric system $(1\text{\ensuremath{-}}x){\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}{\mathrm{TiO}}_{3}\text{\ensuremath{-}}x{\mathrm{BaTiO}}_{3}$ (NBT-BT) continues to pose challenge regarding understanding the mechanisms underlying several interesting phenomena. Issues like (i) whether thermal depoling across compositions is triggered by a structural transformation event or not, (ii) what causes the average Cc structure to partially transform to $R3c$ at $x\ensuremath{\sim}0.03$ in unpoled specimens, (iii) what makes complete depoling of the compositions $0.03\ensuremath{\le}x\ensuremath{\le}0.05$ occur in a considerably small temperature interval as compared to those for $xl0.03$, (iv) what makes the $R3c$-$P4bm$ transition temperature $({T}_{2})$ abruptly become smaller than the depolarization temperature $({T}_{d})$ at $x=0.06$, etc., have remain unresolved. Here, we offer structural insights on these issues by carrying out a detailed investigation using a set of complementary tools involving temperature-dependent x-ray powder diffraction, neutron powder diffraction, dielectric, ferroelectric, piezoelectric, and thermally induced depoling current measurements. We show that onset of thermal depoling in NBT $(x=0)$ well below its depolarization temperature is caused by abrupt reduction of intrinsic polarization in the ferroelectric $R3c$ phase, triggered by the appearance of the $P4bm$ phase. Our study suggests that partial conversion of the Cc average structure to $R3c$ in unpoled NBT-BT at $x\ensuremath{\sim}0.03$ (more precisely in the range $0.03\ensuremath{\le}x\ensuremath{\le}0.05$) is catalyzed by the appearance of $P4bm$ phase. The overlap of ${T}_{d}$ and ${T}_{2}$ for this composition range is correlated with the collapse of the tetragonality of the $P4bm$ phase and significantly reduced kinetic barrier associated with the $R3c\ensuremath{\rightarrow}P4bm$ transformation. We show that the abrupt crossover between ${T}_{d}$ and ${T}_{2}$ at $x=0.06$ is due to takeover of the thermal depoling process by an emergent tetragonal $(P4mm)$-like ferroelectric distortion. We present updated phase diagrams of poled and unpoled specimens which highlight all the subtle details needed to explain the temperature-dependent properties of this complex piezoelectric alloy system.