The Washita Battle has already been mentioned, and all you need to do is look at that fight and you’ll see why Custer did what he did at the LBH. Add to that the fact that the indians would normally withdraw to protect their families. Factor in the Battle of the Rosebud, and you have the recipe for a perfect mess. Was Custer a glory seeker? Oh yeah. Best plan was to probably hit the village with everything he had at the south end and get them moving. But, then you spend the rest of the summer chasing them because even with women and children, the indians could move fast. Not sure there is a good solution in this for old Custer. As was already mentioned, raise a glass to both sides. The indians won the battle, but the wrath from the US after the fight ensured that the indians would not just be defeated, they would be taught a harsh lesson...and they were. A great story because it includes all of the human emotions.
I recently read a book (I'd cite it if I could remember, but they're all starting to blur together - sorry) and the author's position was that Custer was fixated on keeping the indians from scattering, for the reason you stated.
Custer's troops had marched the entire previous day, followed by an all-night forced march, with the intention of resting up before launching a dawn attack the next day, but he believed they had been discovered by the indians and therefore opted to attack immediately - with exhausted horses and men. He did this because he believed the indians were about to scatter.
As they approached LBH, they found the recently abandoned indian camp with the body of the indian killed at the Rosebud - Custer takes this as evidence that the enemy is indeed scattering, so he moved even faster. To make a long story short, the author believed Custer was most worried about scattering indians and didn't really give a thought about the indians going on the offensive until he looked up to see Crazy Horse and Co. riding him down.
That's one theory anyway...