The infinite layer structure type has been known to host high-temperature superconductivity since the discovery of ${\mathrm{Ca}}_{0.86}{\mathrm{Sr}}_{0.14}{\mathrm{CuO}}_{2}$, yet little progress has been made to synthesize many analogs. Here, using ${\mathrm{SrFeO}}_{x}$ as a prototype system, we explore the thermodynamic obstacles behind the scarcity of $3d$ elements adopting the infinite layer structure type. In this context, synthetic considerations to achieve the $AB{\mathrm{O}}_{3}$ to $AB{\mathrm{O}}_{2}$ transformation are discussed. Specifically, we demonstrate that the conventionally reported topochemical reduction can result in hydride incorporation into $\mathrm{SrFe}{\mathrm{O}}_{2}$, causing a decrease in the magnetic ordering temperature of the infinite layered oxide. First-principles simulations further confirm that the incorporation of H is necessary for stabilizing the $\mathrm{SrFe}{\mathrm{O}}_{2}$ phase by decreasing the thermodynamic cost of individual steps required to transform $\mathrm{SrFe}{\mathrm{O}}_{3}$ into $\mathrm{SrFe}{\mathrm{O}}_{2}$, and is the driving factor behind the changes in magnetic exchange interactions that ultimately change the N\'eel temperature (${T}_{\mathrm{N}}$). Additionally, inspired by recent reports of superconductivity in another low-dimensional oxide ${\mathrm{Nd}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{NiO}}_{2}$, ${\mathrm{Sr}}_{0.95}{\mathrm{Nd}}_{0.05}{\mathrm{FeO}}_{2}$ was synthesized via a more traditional topochemical reduction procedure. Both physical characterization and accompanying density-functional theory calculations show that this $A$-site doping can have similar effects on $A{\mathrm{FeO}}_{2}$ stability and magnetic ordering temperatures as with the incorporation of hydrogen. Ultimately, these results suggest that charge doping either through the incorporation of H or $A$-site substitution may be fruitful routes in tuning stability and magnetic properties, with direct consequences on superconducting behavior.