Illusionary Summoner is a card that seems great at first, then seems terrible, and then seems great. For the price of a single sacrificed monster(which cannot be the Illusionary Summoner) you can special summon a Blue-Eyes Ultimate Dragon until the end of the turn. You get a Devil Franken without that nasty drawback of paying 5000 LP.
However, a player will quickly notice the problem with this: if your opponent attacks the Summoner, the effect will trigger on your opponent's turn, and you will simply have a large wall in play until the end of the turn, instead of an offensive machine of destruction.
There are few cards in the game that would allow the Illusionary Summoner to survive your opponent's turn without flipping. Mirror Force and Attack Nullification work, but if your traps are destroyed before the Battle Phase they are useless. The great thing about Military Movements is that, like Missionary of Peace, it can be activated at any time during the turn you want to use it.
While it lacks in speed compared to the Devil Franken combo, it more than makes up for this loss with the safety provided by being allowed to hang on to your precious LP. I wouldn't try to make an actual Devil Franken deck with this, but it's a nice little damage technique that can be slung into most decks. Try it out and see how it works! ^_^