What is the purpose of switching both load and neutral lines of AC power as opposed to just switching the load wire?
The purpose is to isolate the circuit such that no voltage is present on the live or neutral to make it safe for maintenance etc.. As @Incnis Mrsi says you can't take the potential on neutral for granted, the system may have earth sat between live and neutral (where earth may be to a centre tap on the substation transformer) or there may just be significant volts between neutral and earth where you are on the circuit (this is common where the supply doesn't provide an earth).
It is worth noting that for these reasons it is quite possible to trip an incoming RCD if you touch neutral.
One shouldn’t take a low potential on the N wire for granted. If this wire failed (got open) somewhere between the source and consumer, with some load present between N and L, then the N conductor will effectively become live in a part of the grid connected to the load. Think of it as of extreme case of voltage divider:
source N———————— (fail) ————————————[ ]
all voltage drops here live!