It seems that support orders confer several benefits over march orders.
- The support troops won't be destroyed if the fight goes badly.
- The support troops won't be routed if the fight goes badly.
- The support troops can be used in multiple fights in the round.
It seems that a good strategy might be initiate combat with a single infantry, and use the support troops on an adjacent territory to the one you're attacking.
The sole reason I can think that you might not do this, is if on the following turn you want to march your entire army again to a territory that is only accessible from the newly conquered territory.
Is my understanding of these rules correct? - What are the downsides of using support over march orders?