Performing any right-click action silently resets the attack cooldown

The bug

When a player "uses" an item (or performs any other right-click action), the player is put into attack cooldown, as though the player had just attacked. On top of being unintended behavior, this cooldown is not visually indicated: the item in the main hand does not move down, and the attack indicator does not appear. Should the player attack right after a "use" action, the weapon will look like it's doing a normal attack, but will suffer all the penalties of being on cooldown, e.g. reduced damage, no sweeping hit, no crit.

How to reproduce

Put a sword in the main hand, a fishing rod in the offhand, and a mob in front of you. Use the rod, then immediately swing. There's no sweeping attack, and the mob will take less damage.

This bug interferes with common combat scenarios such as: 
-Pulling a shield up to block just before attacking
-Placing blocks/water/lava from offhand then attacking
-Throwing a projectile from offhand then attacking
-Launching self with a wind charge before attacking