Not all matza is hard. And hard matza is a recent development.
From the "Encyclopedia of Jewish Food" (by Rabbi Gil Marks):
"Cracker-like matza was actually a relatively late development, emerging perhaps around the fifteenth century in Ashkenazic communities. The original style of soft matza is still made by many Mizrachi and some Sephardim. Similarly, Ethiopian Jews make a soft matza called kita for Fassikah (Passover). Sephardim call thick matzas by the name boyos (from the Spanish bollo, meaning "bun/small cake") and thinner ones maniuo; the latter were generally used for cooking."
Correct. This is why “Hillel’s sandwich ,” in which horseradish root and lettuce is sandwiched between two matza pieces, is so impractical, crummy, and unpleasant. Back in Hillel’s time, the matzah resembled a fluffy pita - and they would eat the Pascal Offering with it. Hence the original, true Hillel sandwiches were actually delicious pita burgers with just-cooked, juicy steak, fresh lettuce, and horseradish nestled inside...