Cavalry charge without stirrups?

[Titus Marcellus Scato]

Indeed. The introduction of the saddle increased the effectiveness of shock cavalry. It didn't 'allow the creation of' shock cavalry.

With a saddle to brace against, the rider can deliver a slightly stronger blow with his couched spear (lance) and the risk of being unhorsed is reduced. So the saddle was a good invention, but not a critical one. The main benefit of the saddle was to make the training of new recruits a bit quicker (with a saddle, the rider doesn't have to be quite so skilled (well trained) to be effective at shock action.)

Without a saddle, and charging at full gallop, the rider would normally need to help keep his seat by absorbing some of the shock of impact by moderating the blow of his couched lance. This can be done by pulling back slightly on the lance just before the tip makes contact. Alternatively, if the horse is travelling more slowly, the lancer can increase the weight of his strike by 'punching' the lance forward just before impact.

Read this article for an excellent examination of the physics of shock action.

http://www.classicalfencing.com/articles/shock.php