While there were some (elaborately decorated) cross-guards invented in the Edo period called katanatsuba (刀鍔) and another type called mamorokobushi (護拳) katanas generally lacked cross guards and hand protections for the simple reason that they were quick withdraw* (not primarily for thrusting however, as I've been corrected) weapons, whereas European swords with the exception of rapiers (which usually have hilts like 刀鍔) were usually broad weapons.

Japan had a different style of combat with the sword--Katanas were quick withdraw weapons, meant to be compatible with a Japanese concept called Ieaidou (居合道). The Japanese have developed a whole artform around this concept of swordplay, and it has developed into the sword tradition that Japan has today, with a focus on quick movements as opposed to slower, heavier striking.

They had no need to - the tsuba was more than enough function as a guard to protect the wielder's hand, as the various other functions of larger crossguards (e.g. to lock swords) were not seen in most styles. A small, round disc to simply ensure you didn't accidentally slip was all that was needed. Swordsmiths were (relatively) more focused on the design of the blade itself, such as the curvature of blades (which you can definitely see the progression of in naginata and katana), were of a larger concern. You could mention too that the katana, being a primarily slashing weapon (note - primarily), combined with how it was used against its contemporary armour counterparts, meant that a larger crossguard had no specific function or significant advantage over a smaller one, such as the tsuba. Not even to mention that the katana was rarely used anyway.

Swords are designed for specific styles of fencing and combat. Also, while a crossguard protects your hand, it also hinders your movements, determining how you attack and defend.

A related question - why would Japanese swordsmen just attack the hands of someone wielding a Japanese sword?

I come from a fencing background, and in Sabre and Epee (weapons where the hand is target), the hand could be considered one of the main targets to go for (cus it's closer). These sport weapons have much more complete guards that protect the entire hand much more than the Japanese tsuba - yet hands still get hit all the time, with both a cut in sabre and a thrust in epee.

It seems to me like it would be strangely easy to strike the hands (namely the part holding the sword, not the wrists) of someone holding a japanese sword. What prevents this? Is it cultural? Or is there a technique or something that makes it a poor strategy?