Within certain tolerances, varying flight height can actually be helpful, especially for 3D and elevation modeling. You can think of it as a sampling problem: by sampling different heights, you get better sampling information about height, and improve your model.
Typically, we fly at a single height either a single height above ground surface or the flight origin for a couple of reasons. For the rest of the paragraph, I will be guessing at what DroneDeploy and MapsMadeEasy or trying to accomplish with their recommendations. Flying a single height above the origin, if we have some variation in terrain heights and trees and buildings etc, gives us some of that variation in effective height that helps us get better 3D and elevation data. It doesn’t work well in very flat areas to do this, but is good in many circumstances, and is simple to flight plan. Flying at a single height above ground gives us even sampling across our study area, and ensures that, for ground pixels anyway, we have a know sampling resolution and optimizes for better XY sampling.
DroneDeploy and MapsMadeEasy are platforms that are trying to optimize the quality of the outputs of the datasets processed through their platforms in different ways, but the reality is, you can decide your own requirements, and fly accordingly. That said, I almost always vary height or height and camera angle, because correcting for distortion in Z aids a lot the overall quality of any imagery collected.