Here’s an eight part series by a historian on which parts of the battle are realistic within the world and which are not, in case that kind of thing is interesting to you:

https://acoup.blog/2020/05/01/collections-the-battle-of-helms-deep-part-i-bargaining-for-goods-at-helms-gate/

He had sappers. And yeah Pike beats horse.

The Battle of Helm’s Deep is full of very obvious errors. There is an awesome Dutch historian, Roel Konijnendijk, who trashes movies for fun that talks about it:

https://www.youtube.com/watch?v=xPGdOXstSyk

My favourite one is when they are shouting orders to eachother. There is no way for the Elven archers to hear Aragorn’s commands, or for Aragorn to hear Theoden’s fallback order.