Well, it exposes you to attack on the battlefield. Saxons don't normally worry about knightly codes as such, but they generally focus their attacks on the knights and let the squires be as a lesser threat. In the thick of battle, you are likely to be engaged with an enemy. It's hard to break off to go rescue someone who was unhorsed while battling for your life. Forgoing an attack / defence to toss someone a spare spear may cost you your own life. And if you are engaged in battle, it will be hard to break off to drag an unconscious comrade to safety.
There is a reason knights employ squires who's sole duty is to perform those tasks as required - spare weapons, spare horses, escape to safety if required, etc.
Now, you could gear down some of your party, make them appear less threatening and have them fill the role of a squire. But that will cost them glory if and when you do see battle. A squire's job is important, but it does not earn much in the way of glory.
In the Arthurian legends (not IC knowledge), there is a story of two knights who were travelling without squires. They met on the road and became involved in a duel. They fought, each one scoring hits against the other. They were evenly matched, and each one pushed harder and harder to win. Soon the friendly duel drew blood. Eventually, exhausted and bleeding, all they could do was lie in the dirt and watch each other bleed out. Both knights died, whereas if either one of them had brought a squire, both might have lived.
