This exercise got me looking for the Weathstone bridge, but the more I look at it the more I cannot find any use for it nowdays.
Any op-amp circuit like a non inverter would do a better job...
As I see it the Weathstone bridge is just a good exercise for beginners to learn the Kirchhoff law
Bridges are important still today for high precision instrumentation.
The beayty of bridge circuit is that is provides integrated high stability voltage reference (assuming one unknown) and passive (pseudo) amplifier.
It also still can be made to be totally passive so no interference from electronic amplifier and it is also considered instrically safe for EX-spaces ie. with Pt100.
It definedly is not a mainsteam, but it have never been mainstream.
It is one of those rare circuits which can be used to push the limit further than the used components by iteration.
Ps. The common "equation" floating around is oversimplification when effect of sensing device is assumed to be zero ie. infitely high resistance over the bridge halfs and equilibrium state.