Slashing with Short Swords

Can a short sword be used to deal slashing damage?

The Weapons Table seems to list short swords as having only the damage type of piercing, and lacking the slashing damage type. However, this strikes me as either a mistake or a misguided decision. Short swords are typically described as and visually depicted as having a double-edged blade, which should mean that it is able to cut.

From The Forgotten Realms wiki (emphasis mine):

In essence, this weapon is a smaller version of the longsword but longer than a dagger or dirk, having many of the same parts including a generally double-edged blade, cross-guard, grip, and pommel. The blade is typically from 12 to 20 in (30 to 50 cm) long with a sharp point. An average short sword costs 10 gp and weighs 2 lb (0.9 kg).1 First edition D&D defined the short sword as “all pointed cutting & thrusting weapons with blade length between 15 in (38 cm) and 24 in (61 cm).”2

Other 3rd Edition material also described as being effectively between the length of a longsword and a daggerboth of which are capable of slashing – suggesting that, all other properties the same, it should be able to as well.

I’ve heard some arguments that the short sword is intended to model certain historical weapons, such as the gladius, which were primarily used for stabbing by Roman soldiers after the reach of their spears had been breached. Even so, the gladius also sported a double-edged blade and seemed capable of slashing if necessary.

Of course, this problem only comes into play when fighting a monster with damage resistances or vulnerabilities to one damage type over the other. Even if the weapon was not primarily designed for slashing (which still seems in question), I would think that under such circumstances of life and death, at the very least, this would be possible.

Is there any reason, historical or otherwise, as to why a character could not slash with a short sword?