The big reason to do strat battles for me is the experience.. not only actually learning the ropes but you get a lot of actual character experience as well.
Even if you demand money they don't have to pay you, as has been said. If you request a small amount of money and do alright, you'll likely be paid.
Keep in mind that you're 100% fighting with their equipment (which they bought) and their soldiers (which they pay for) so you're contributing a warm body, in essence. If you use a lot of their tickets (soldiers) and overall don't accomplish much, that will eat into your possible earnings.
Edit: Also, pick up weapons off the battlefield. Your commander will appreciate it.