Why didn't more ancient armies use the Spartan shield?

A post of mine about the Riders of Rohan quotes a little bit of John Keegan’s famous analysis of cavarly vs infantry from his terrific book, The Face of Battle:

Horsemen effective psychologically against low-morale infantry, less so against “firm” infantry, almost impotent against really good infantry.

Don’t take my word for it, though – read the book. It’s not too dense, and he really has some incisive thoughts about what really went down on the battlefield as opposed to the layers of myth with which we’ve encrusted these things.

Here’s something about defending against cavalry I never understood. In movies and such, they always attack the horseman, presumably because you’re clearly not allowed to hurt or endanger the horses on a set, but it always seemed to me that in reality it should be much easier to just kill the horse. Spear through the chest, chop at the legs, there’s tons of ways to grievously injure a horse on an ancient battlefield. It’s clearly a much bigger target and in going down could potentially kill or seriously injure the rider; at the very least the rider will be stunned long enough to jam a spear into him.

I understand that horses were financially and strategically valuable, and it would certainly be a part of the spoils of war to capture your enemy’s horses, but is there some other reason I’m not seeing to spare the horses on the battlefield?

Not really. On the other hand, on the battlefield, the horse would be stomping, biting, and kicking, too. And armored.

Different era but at the Battle of Waterloo (see the early 1970s film with Rod Steiger and Christopher Plummer) when Napoleon’s cavalry attacks the British, they form up into squares and the horses won’t charge the bayonets. Great aerial photography on that scene