Mash out was conceived in the decoction method. In the decoction process, a grain bed filter is formed and extract is drawn by fly sparging. Lautering might take a couple of hours, depending on the thickness of the grain bed and mash viscosity. To stop enzymatic activity during lautering, enzymes were thermally denatured.
Using the English method a brewer is limited when it comes to controlling enzymatic action. It is a take what you get process, based on a single conversion temperature, pH stuck on one number, time and whatever the mash thickness is during conversion. When mash out is added to the English process, the hard starch that is stuck in the ends of the husk begins to burst around 169F. The excess starch goes into solution, enzymatic action ceases due to thermal denaturing. Excess starch is washed down the line into the final product. That might not be a problem when the brew goes from boiler to belly in 4 to 6 weeks, but in a lager or pils, excess starch reduces stability, unless it is dealt with upstream. Doing a 10 minute vorlauf with mash at 170F would stretch out the process to 20 minutes. Adding more starch to the solution.
Here's the thing. Depending at what temp was chosen for conversion and for how long the rest would be, will determine how long beta was active. In temp ranges in the low 150s, beta denatures quickly. After beta denatures, alpha continues to create non-fermentable sugar. The action might cause the beer to be imbalanced, finishing at a higher gravity than expected. In that case, mashing out would be a good idea, stopping enzymatic action. Mash out reduces viscosity, which helps when it comes to fly sparging. Mash out is usually done after conversion, but not always. By controlling enzymes the final product will be affected.