The trinket slot is an optional equipment slot, only unlocked by spending energy to do so. This makes trinkets a viable vector for exploring unique or unusual effects.
Consider the following:

A set of three trinkets that affect probabilities of hearts, crowns, and heat that drop from defeated enemies. Each trinket increases the amount of one at the expense of the other two. Balance considerations will have to be given regarding how many hearts equals how many crowns equals how much heat.

A set of three trinkets that causes a certain percentage of damage dealt to be turned into piercing, elemental, or shadow. The total amount of damage from the weapon is not changed. These trinkets allow a player to turn all of their weapons into dual-type damage (or possibly even triple-type damage), allowing for greater versatility in damage types without requiring that a player uses a weapon that naturally generates a given damage type.

I feel that both of these trinket sets offer players an opportunity to spend resources to acquire an unusual change, rather than to simply make a number bigger.