Stirrers are generally seen in the HLT when the HLT is used for a HERMS. You will have a heat source, and you will have a coil for the HERMS that will extract heat. Since you have these two opposing forces, a stirrer is required so that your water is homogenous in temperature. Otherwise the HERMS coil will create a cold spot around itself from extracing heat, the element will create a hot spot, and your thermowell will have no idea what the TRUE temp is inside the HLT.
In a standard HLT, a stirrer is not required.